Question

Prove that the value of the expression does not depend on the variable x:

a) (x–5)(x+8)–(x+4)(x–1)
b) x^4–(x^2–1)(x^2+1)

PLEASE HELP 20 POINTS

Answer 1

See below

Explanation:

If an expression is not dependent on x, it simplified form must not contain x. To show that this is the case for (a) and (b) we need to simplify them and assess:

(a)

`(x-5)(x+8)-(x+4)(x-1)=\\=x^2-5x+8x-40-x^2-4x+x+4=-36`

Indeed, does not depend on x!

And (b)

`x^4-(x^2-1)(x^2+1)=x^4-x^4+x^2-x^2+1=1`

Again, does not depend on x.