Multiply each expression.3a(5a+3b)3a(5a+3b)

15 a 2 + 9 a b 15a^2+9ab 15 a 2 + 9 ab

Multiply each expression. 3 a ( 5 a + 3 b ) 3a(5a+3b)

For this problem, we want to multiply our monomial by this polynomial. And to do that, we're going to use our distributive property by multiplying in this outside term into each of the terms in the sum. So doing that, we'd get three a times five a plus three a times three b. And now we're going to continue simplifying by combining our like factors. We have three and five, which can combine to make 15, and a times a combines to make a squared. And for our second factor, we have three and three that are alike, which combine to make nine. And then a and b are not alike. And so those will stay as a times b. So all in all, this simplifies to 15 a squared plus nine times a times b.

Multiply each expression. 3 a ( 5 a + 3 b ) 3a(5a+3b)

15 a 2 + 9 a b 15a^2+9ab 15 a 2 + 9 ab

9 a 2 + 15 a b 9a^2+15ab 9 a 2 + 15 ab

9 a 2 + 9 a b 9a^2+9ab 9 a 2 + 9 ab

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.
$3 a (5 a + 3 b)$

$15 a squared plus 3 a b$

$9a^2+15ab$

$15a^2+9ab$

$9a^2+9ab$

Verified step by step guidance

Identify the monomial and the polynomial in the expression you need to multiply. For example, if you have a monomial like \$3x$ and a polynomial like $2x^2 + 5x - 4$, recognize these parts clearly.

Apply the distributive property, which means you multiply the monomial by each term inside the polynomial separately. This can be written as \$3x \cdot (2x^2) + 3x \cdot (5x) + 3x \cdot (-4)$.

Multiply the coefficients (numbers) together and then multiply the variables by adding their exponents. For example, \$3 \cdot 2 = 6$ and $x \cdot x^2 = x^{1+2} = x^3$.

Repeat the multiplication for each term: multiply \$3x$ by $5x$ and then by $-4$, remembering to handle the signs correctly.

After multiplying each term, write the resulting terms together to form the new polynomial. This is your product of the monomial and polynomial.

3:46m

Watch next

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

Start learning