# Multiplying Polynomials - Video Tutorials & Practice Problems

## FOIL

Multiply the polynomials using FOIL. $\left(x-5\right)\left(x-12\right)$

$x^2-12x+60$

$x^2-17x+60$

$x^2-5x+60$

$x^2-17x-60$

Multiply the polynomials using FOIL. $\left(4x+7\right)\left(-x+6\right)$

$4x^2+17x+42$

$4x^2+31x+42$

$-4x^2+17x+42$

$-4x^2-x+42$

Multiply the polynomials using FOIL. $\left(x^2-3x\right)\left(2x+8\right)$

$2x^2+2x-24$

$2x^3+2x^2-6x-24$

$2x^3-2x^2-24x$

$2x^3+2x^2-24x$

## Multiply Polynomials Using the Distributive Property

Multiply the polynomials. $\left(x+4\right)\left(3x^2-2x+1\right)$

$3x^3+10x^2-7x+4$

$3x^3+12x^2+x+4$

$12x^2-8x+4$

$3x^3-2x^2+x$

Multiply the polynomials. $\left(x+3\right)\left(x-5\right)\left(-2x+1\right)$

$x^2-2x-15$

$-2x^3+4x^2+30x$

$-2x^3+5x^2+28x-15$

$2x^3+5x^2+28x-15$

## Special Products - Square Formulas

Multiply the polynomials using special product formulas. $\left(5x-9\right)\left(5x+9\right)$

$5x^2-81$

$25x^2-81$

$25x^2+90x+81$

$25x^2-90x+81$

Multiply the polynomials using special product formulas. $\left(3x+5\right)\left(3x+5\right)$

$9x^2+15x+25$

$9x^2+25$

$9x^2+30x+25$

$9x^2+55$

## Special Products - Cube Formulas

Multiply the polynomials using special product formulas. $\left(2x+4\right)^3$

$8x^3+16x^2+32x+64$

$8x^3+24x^2+24x+64$

$8x^3+48x^2+96x+64$

$x^3+24x^2+96x+64$

## Do you want more practice?

- In Exercises 1–8, multiply the monomials. (3x²)(5x⁴)
- In Exercises 1–4, is the algebraic expression a polynomial? If it is, write the polynomial in standard form. 2...
- Evaluate each algebraic expression for the given value or value(s) of the variable(s). 3+6(x-2)^3 for x=4
- In Exercises 1–4, is the algebraic expression a polynomial? If it is, write the polynomial in standard form. (...
- Fill in the blank to correctly complete each sentence. In the term -6x^2y, -6 is the ______.
- In Exercises 1–6, find all numbers that must be excluded from the domain of each rational expression. (x−1)/(x...
- In Exercises 5–8, find the degree of the polynomial. x^2−4x^3+9x−12x^4+63
- In Exercises 7–14, simplify each rational expression. Find all numbers that must be excluded from the domain o...
- In Exercises 9–22, multiply the monomial and the polynomial. 4x²(3x+2)
- In Exercises 7–14, simplify each rational expression. Find all numbers that must be excluded from the domain o...
- In Exercises 9–22, multiply the monomial and the polynomial. 2y(y²−5y)
- Identify each expression as a polynomial or not a polynomial. For each polynomial, give the degree and identif...
- In Exercises 9–22, multiply the monomial and the polynomial. 5x³ (2x⁵−4x²+9)
- In Exercises 9–14, perform the indicated operations. Write the resulting polynomial in standard form and indic...
- Identify each expression as a polynomial or not a polynomial. For each polynomial, give the degree and identif...
- In Exercises 7–14, simplify each rational expression. Find all numbers that must be excluded from the domain o...
- Identify each expression as a polynomial or not a polynomial. For each polynomial, give the degree and identif...
- In Exercises 15–58, find each product. (x+1)(x^2−x+1)
- In Exercises 15–32, multiply or divide as indicated. (6x+9)/(3x−15) ⋅ (x−5)/(4x+6)
- In Exercises 15–58, find each product. (2x−3)(x^2−3x+5)
- In Exercises 15–58, find each product. (x+7)(x+3)
- In Exercises 15–32, multiply or divide as indicated. (x^3−8)/(x^2−4) ⋅ (x+2)/3x
- In Exercises 9–22, multiply the monomial and the polynomial. −4xⁿ (3x²ⁿ − 5xⁿ + 1/2 x)
- In Exercises 23–34, find each product using either a horizontal or a vertical format. (x−3)(x²+2x+5)
- Add or subtract, as indicated. See Example 2. (5x^2-4x+7) + (-4x^2+3x-5)
- Add or subtract, as indicated. See Example 2. (3m^5-3m^2+4) + (-2m^3-m^2+6)
- In Exercises 23–34, find each product using either a horizontal or a vertical format. (x−1)(x²+x+1)
- In Exercises 15–32, multiply or divide as indicated. (x^2−4)/(x−2) ÷ (x+2)/(4x−8)
- In Exercises 15–58, find each product. (2x−5)(7x+2)
- In Exercises 15–32, multiply or divide as indicated. (x^2+x)/(x^2−4) ÷ (x^2−1)/(x^2+5x+6)
- In Exercises 15–58, find each product. (7x^2−2)(3x^2−5)
- In Exercises 15–58, find each product. (7x^3+5)(x^2−2)
- Find each product. See Examples 3–5. (5m-6)(3m+4)
- In Exercises 15–32, multiply or divide as indicated. (x^2−4)/(x^2+3x−10) ÷ (x^2+5x+6)/(x^2+8x+15)
- Find each product. See Examples 3–5. x^2(3x-2)(5x+1)
- In Exercises 15–32, multiply or divide as indicated. (x^3−25x)/4x^2 ⋅ (2x^2−2)/(x^2−6x+5) ÷ (x^2+5x)/(7x+7)
- Find each product. See Examples 3–5. 4x^2(3x63+2x^2-5x+1)
- In Exercises 23–34, find each product using either a horizontal or a vertical format. (xy+2)(x²y²−2xy+4)
- In Exercises 29–40, add the polynomials. Assume that all variable exponents represent whole numbers. (7x²y − ...
- In Exercises 33–68, add or subtract as indicated. (3x+2)/(3x+4) + (3x+6)/(3x+4)
- In Exercises 29–40, add the polynomials. Assume that all variable exponents represent whole numbers. (5x²y + ...
- In Exercises 35–54, use the FOIL method to multiply the binomials. (x+5)(x+8)
- In Exercises 29–40, add the polynomials. Assume that all variable exponents represent whole numbers. (9x⁴y² −...
- In Exercises 35–54, use the FOIL method to multiply the binomials. (y+5)(y−6)
- Find each product. See Examples 3–5. (m-n+k)(m+2n-3k)
- Find each product. See Examples 3–5. (r-3s+t)(2r-s+t)
- Find each product. See Examples 3–5. (2x+3)(2x-3)(4x^2-9)
- In Exercises 35–54, use the FOIL method to multiply the binomials. (5x+3)(2x+1)
- In Exercises 33–68, add or subtract as indicated. 5/x + 3
- In Exercises 15–58, find each product. (x+5)^2
- In Exercises 33–68, add or subtract as indicated. 3x/8 + x/12
- Find each product. See Examples 5 and 6. (8s-3t)(8s+3t)
- In Exercises 35–54, use the FOIL method to multiply the binomials. (2x−3)(4x−5)
- In Exercises 15–58, find each product. (x−3)^2
- Find each product. See Examples 5 and 6. (4x^2-5y0(4x^2+5y)
- In Exercises 35–54, use the FOIL method to multiply the binomials. (x−3y)(2x+7y)
- In Exercises 41–50, subtract the polynomials. Assume that all variable exponents represent whole numbers. (x³...
- Find each product. See Examples 5 and 6. (4m+2n)^2
- In Exercises 35–54, use the FOIL method to multiply the binomials. (7xy+1)(2xy−3)
- In Exercises 41–50, subtract the polynomials. Assume that all variable exponents represent whole numbers. (3x...
- In Exercises 33–68, add or subtract as indicated. 2/5x − (x+1)/4x
- In Exercises 41–50, subtract the polynomials. Assume that all variable exponents represent whole numbers. (7y...
- In Exercises 33–68, add or subtract as indicated. (x+9)/10x^3 + 11/15x^2
- Subtract −5a²b⁴ − 8ab² − ab from 3a²b⁴ − 5ab² + 7ab.
- Find each product. See Examples 5 and 6. [(2p-3)+q]^2
- In Exercises 35–54, use the FOIL method to multiply the binomials. (7x³+5)(x²−2)
- In Exercises 33–68, add or subtract as indicated. 3/(x+1) − 3/x
- Find each product. See Examples 5 and 6. [(3q+5)-p][(3q+5)+p]
- In Exercises 35–54, use the FOIL method to multiply the binomials. (3xⁿ−yⁿ)(xⁿ+2yⁿ)
- Find each product. See Examples 5 and 6. [(9r-s)+2][(9r-s)-2]
- In Exercises 55–68, multiply using one of the rules for the square of a binomial. (x + 3)²
- In Exercises 33–68, add or subtract as indicated. 3x/(x−3) − (x+4)/(x+2)
- In Exercises 55–68, multiply using one of the rules for the square of a binomial. (y − 5)²
- In Exercises 15–58, find each product. (2x−3)^3
- Find each product. See Examples 5 and 6. (z-3)^3
- Find each product. See Examples 5 and 6. (q-2)^4
- Find each product. See Examples 5 and 6. (r+3)^4
- In Exercises 59–66, perform the indicated operations. Indicate the degree of the resulting polynomial. (7x^4 y...
- Perform the indicated operations. See Examples 2–6. -3(4q^2-3q+2) + 2(-q^2+q-4)
- In Exercises 59–66, perform the indicated operations. Indicate the degree of the resulting polynomial. (3x^4 y...
- In Exercises 55–68, multiply using one of the rules for the square of a binomial. (4xy² − xy)²
- Perform the indicated operations. See Examples 2–6. 2(3r^2+4r+2) - 3(-r^2+4r-5)
- In Exercises 55–68, multiply using one of the rules for the square of a binomial. (aⁿ + 4bⁿ)²
- Perform the indicated operations. See Examples 2–6. m(5m-2) + 9(5-m)
- In Exercises 69–82, multiply using the rule for the product of the sum and difference of two terms. (x + 4)(x...
- In Exercises 67–82, find each product. (3x−y)(2x+5y)
- In Exercises 67–82, find each product. (7x^2 y+1)(2x^2 y−3)
- Perform the indicated operations. Write the resulting polynomial in standard form and indicate its degree. (-6...
- In Exercises 69–82, multiply using the rule for the product of the sum and difference of two terms. (4x + 7y)...
- In Exercises 69–82, multiply using the rule for the product of the sum and difference of two terms. (8x + 7y)...
- In Exercises 67–82, find each product. (9x+7y)^2
- Find each product : (3x-2)(4x^2+3x-5)
- In Exercises 69–82, multiply using the rule for the product of the sum and difference of two terms. (y³ + 2)(...
- Find each product. Assume all variables represent positive real numbers. (x+x^1/2)(x-x^1/2)
- In Exercises 69–82, multiply using the rule for the product of the sum and difference of two terms. (y³ + 3)(...
- In Exercises 67–82, find each product. (x−y)(x^2+xy+y^2)
- Find each product. Assume all variables represent positive real numbers. (p^1/2-p^-1/2)(p^1/2+p^-1/2)
- In Exercises 69–82, multiply using the rule for the product of the sum and difference of two terms. (3xy² − 4...
- In Exercises 67–82, find each product. (7xy^2−10y)(7xy^2+10y)
- In Exercises 69–82, multiply using the rule for the product of the sum and difference of two terms. (5aⁿ − 7)...
- Find each product. (x+7y)(3x-5y)
- In Exercises 83–94, find each product. (x + y + 3)(x + y − 3)
- Find each product. (7x+4y)(7x-4y)
- Find each product. (a-b)(a^+ab+b^2)
- In Exercises 83–90, perform the indicated operations. Simplify the result, if possible. (y^−1−(y+2)^−1)/2
- In Exercises 83–90, perform the indicated operation or operations. (2x−7)^5/(2x−7)^3
- In Exercises 83–94, find each product. (x + 1)(x − 1)(x² + 1)
- Exercises 108–110 will help you prepare for the material covered in the next section. Multiply: (2x³y²)(5x⁴y⁷...
- Exercises 108–110 will help you prepare for the material covered in the next section. Simplify and express th...
- The special products can be used to perform selected multiplications. On the left, we use (x+y)(x-y) = x^2-y^2...
- In Exercises 121–128, write each English phrase as an algebraic expression. Then simplify the expression. Let ...
- In Exercises 121–128, write each English phrase as an algebraic expression. Then simplify the expression. Let ...
- In Exercises 117–130, simplify each algebraic expression. 8(3x-5)-6x
- In Exercises 117–130, simplify each algebraic expression. 5(3y-2)-(7y+2)
- In Exercises 117–130, simplify each algebraic expression. 7-4[3-(4y-5)]
- In Exercises 152–153, a polynomial is given in factored form. Use multiplication to find the product of the fa...