Question

Using the distributive property to find the product (y−4x)(y2 4y 16) results in a polynomial of the form y3 4y2 ay−4xy2−axy−64x. what is the value of a in the polynomial? 4 8 16 32

Answer 1

The product  (y−4x)(y^2 + 4y + 16) results in a polynomial of the form y3 4y2 ay−4xy2−axy−64x then the value of a is 16.

What is distributive property?

The distributive property states that an expression of the form A(B + C) can be solved by a multiplication over addition operation that is

A(B + C) = AB + AC

This property is known by distributive law and applies to subtraction also.

First let w = y-4x make distribution a bit easier

(y−4x)(y^2 + 4y + 16)

$w(y^2 + 4y + 16)\\wy^2 + w4y + w16$

now put the values of w in the equation

$(y-4x)y^2 + (y-4x)4y + (y-4x)16\\y^3-4xy^2 + 4y^2-16xy+16y-64x$

Here the value of a is 16.

Learn more about the distributive property:

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