Question

Angelina factored (x - 4)8 and wrote that it was equal to (x2 - 42)2(x2 + 42). Use complete sentences to explain how you could confirm whether Angela’s solution is correct. Prove your conclusion mathematically.

Answer 1

to calculate what Angelina wrote. =(x^-16)^2(x^2+16)

=(x^2)^2-2x^2*16+16^2

=(x^4-32x^2+256)(x-16)

=x^4x^2+x^2*16+(-32x^2)x^2+(-32x^2)*16+256x^2+256*16

=x^6-16x^4-256x^2+4096

can see that first term is x^6.

But for (x - 4)^8 expression, first term should be x^8.

So say that Angela’s solution is incorrect.

Explanation:

Answer 2

There are several ways to confirm that the two expressions are equal. One method is to simply factor the first expression and see it you get a result equal to the second expression. An easier method is to set a value for x and substitute it to the two expressions. If the resulting value is that same, this means that the two expressions are equal.