Question

Simplify (x² + 16)(x² - 16)=​

Answer 1

x⁴ - 256

Explanation:

`\bold{METHOD\ 1:}\\\\(x^2+16)(x^2-16)\qquad\text{use}\ a^2-b^2=(a-b)(a+b)\\\\=(x^2)^2-16^2\qquad\text{use}\ (a^n)^m=a^(nm)\\\\=x^((2)(2))-256\\\\=x^4-256`

`\bold{METHOD\ 2:}\\\\(x^2+16)(x^2-16)\qquad\text{use FOIL:}\ (a+b)(c+d)=ac+ad+bc+bd\\\\=(x^2)(x^2)+(x^2)(-16)+(16)(x^2)+(16)(-16)\qquad\text{use}\ a^n\cdot a^m=a^(n+m)\\\\=x^(2+2)-16x^2+16x^2-256\qquad\text{cancel}\ 16x^2\\\\=x^4-256`

Answer 2

x^4 - 256

Explanation:

We learn that: a^2 + b^2 = (a+b) * (a-b) so in this case:

(x² + 16)(x² - 16)

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

= x^4 - 256

Hope this helped :3