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?

Answer 1

According to the distributive property, multiplying the sum of two or more addends by a number will give the same result as multiplying each addend individually by the number and then adding the products together.

`(a+b)\cdot(c+d)=ac+ad+bc+bd`

Using this property in our product

`(y-4x)(y^2+4y+16)`

we're going to have

`(y-4x)(y^2+4y+16)=y^3+4y^2+16y-4xy^2-16xy-64x`

Comparing this expression to the expression given, we have the value of a.

`\begin{gathered} y^3+4y^2+ay-4xy^2-axy-64x=y^3+4y^2+16y-4xy^2-16xy-64x \\ \Rightarrow a=16 \end{gathered}`