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Chapter 5: Problem 41

Find each product of the monomial and the polynomial. $$-4 y(3 y+5)$$

Short Answer

Expert verified
The product of the monomial and the polynomial, \(-4y(3y+5)\), is \(-12y^2 - 20y\).

Step by step solution

01

Identification of Terms

Firstly, identify the monomial and the polynomial. In this case, the monomial is -4y and the polynomial is 3y+5.
02

Application of Distributive Property

Apply the distributive property by multiplying the monomial by each term in the polynomial. As such, \(-4y \times 3y\) and \(-4y \times 5\) are the two calculations that need to be made.
03

Perform the Multiplications

Multiply the monomial by each term separately. This will entail performing the calculations \(-4y \times 3y = -12y^2\) and \(-4y \times 5 = -20y\)
04

Write out the Answer

The final solution is obtained by combining the results of the multiplications. Write out the equation, \(-12y^2 - 20y\)

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