Question

The product of (4z2 + 7z – 8) and (–z + 3) is –4z3 + xz2 + yz – 24.

What is the value of x? 
What is the value of y?

Answer 1

`\text{The value of x and y is } x=5, y=29`

Explanation:

Given the product of two expressions

`4z^2+7z-8\text{ and }-z+3\text{ is }-4z^3+xz^2+yz-24`

we have to find the value of x and y

First we find the product of

`4z^2+7z-8\text{ and }-z+3`

`(4z^2+7z-8)(-z+3)`

Opening the brackets

`4z^2(-z+3)+7z(-z+3)-8(-z+3)`

Using distributive property, a.(b+c)=a.b+a.c

`(-4z^3+12z^2)+(-7z^2+21z)+(8z-24)`

Combining like terms

`-4z^3+(12z^2-7z^2)+(21z+8z)-24`

`-4z^3+5z^2+29z-24`

which is required product.

`\text{Now compare above product with given product }-4z^3+xz^2+yz-24`

`x=5, y=29`