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

6. Exponents, Polynomials, and Polynomial Functions

Multiplying Polynomials

Intermediate Algebra

6. Exponents, Polynomials, and Polynomial Functions

Multiplying Polynomials

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Multiple Choice

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

$15 a squared plus 3 a b$

$9 a squared plus 15 a b$

$15a^2+9ab$

$9a^2+9ab$

Verified step by step guidance

Identify the expression to multiply: \$3a(5a + 3b)$. This means you will multiply $3a$ by each term inside the parentheses.

Apply the distributive property: multiply \$3a$ by $5a$ and then multiply $3a$ by $3b$. Write this as $3a \times 5a + 3a \times 3b$.

Multiply the coefficients (numbers) together: \$3 \times 5$ and $3 \times 3$.

Multiply the variables using the laws of exponents: $a \times a = a^{2}$ and $a \times b = ab$.

Combine the results to write the expanded expression as \$15a^{2} + 9ab$.

3:46m

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