Multiply each expression.(3x2−5x+3)2x2(3x^2-5x+3)2x^2

6 x 4 − 10 x 3 + 6 x 2 6x^4-10x^3+6x^2 6 x 4 − 10 x 3 + 6 x 2

Multiply each expression. ( 3 x 2 − 5 x + 3 ) 2 x 2 (3x^2-5x+3)2x^2

this problem, we want to multiply these expressions, our monomial two x squared, by our polynomial three x squared minus five x plus three. And to do this, we're going to use our Distributive Property. Even though our monomial is on the right hand side, we can still use this property and distribute it in by multiplying it by each of the terms in this sum. So doing that, we'll get two x squared times three x squared plus two x squared times negative five x, plus two x squared times three. Simplifying, we'll combine all of our common factors. So, first we have two times three, which makes six, and then x squared times x squared makes x to the fourth power. Next, we'll have two times negative five, which makes negative 10, and x squared times x is x cubed. And lastly, we have two times three, which makes six, and x squared by itself is x squared. So this expression simplifies to 6x to the fourth power minus 10x cubed plus 6x squared.

Multiply each expression. ( 3 x 2 − 5 x + 3 ) 2 x 2 (3x^2-5x+3)2x^2

6 x 4 − 10 x 3 + 6 x 2 6x^4-10x^3+6x^2 6 x 4 − 10 x 3 + 6 x 2

6 x 4 + 10 x 3 + 6 x 2 6x^4+10x^3+6x^2

6 x 3 − 10 x 2 + 6 x 6x^3-10x^2+6x 6 x 3 − 10 x 2 + 6 x

6 x 4 − 10 x 2 + 6 x 6x^4-10x^2+6x 6 x 4 − 10 x 2 + 6 x

6. Exponents and Polynomials

Multiplying Polynomials

Beginning Algebra

6. Exponents and Polynomials

Multiplying Polynomials

Struggling with Beginning Algebra?

Join thousands of students who trust us to help them ace their exams!Watch the first video

Multiple Choice

Multiply each expression.
$(3 x^{2} - 5 x + 3) 2 x^{2}$

$6 x^{4} + 10 x^{3} + 6 x^{2}$

$6x^3-10x^2+6x$

$6x^4-10x^2+6x$

$6x^4-10x^3+6x^2$

Verified step by step guidance

Identify the monomial and the polynomial you need to multiply. The polynomial will be a sum or difference of terms, and the monomial is a single term.

Apply the distributive property: multiply the monomial by each term in the polynomial separately. This means you multiply the coefficients and then multiply the variables by adding their exponents.

For each term, multiply the coefficients (numbers) together. For example, if the monomial coefficient is $a$ and the polynomial term coefficient is $b$, multiply to get $a \times b$.

Multiply the variables by applying the rule $x^m \times x^n = x^{m+n}$. If a variable is missing in one term, treat it as having an exponent of zero.

After multiplying each term, write down the resulting terms together to form the final polynomial expression.

3:46m

Watch next

Master Multiply Polynomials by Monomials with a bite sized video explanation from Patrick Ford

Start learning