Given expression: [tex](x - 4)^8[/tex].
Angelina wrote : [tex](x^2 - 4^2)^2(x^2 + 4^2)[/tex].
Let us multipl[tex](x^2 - 4^2)^2(x^2 + 4^2)=\left(x^2-16\right)^2\left(x^2+16\right)[/tex]
[tex]\mathrm{Apply\:Perfect\:Square\:Formula}:\quad \left(a-b\right)^2=a^2-2ab+b^2[/tex]
[tex]=\left(x^2\right)^2-2x^2\cdot \:16+16^2[/tex]
[tex]\:\left(x^2\right)^2-2x^2\cdot \:16+16^2:\quad x^4-32x^2+256[/tex]
[tex]=(x^4-32x^2+256)(\left x^2+16\right)[/tex]
[tex]\mathrm{Distribute\:parentheses}[/tex]
[tex]=x^4x^2+x^4\cdot \:16+\left(-32x^2\right)x^2+\left(-32x^2\right)\cdot \:16+256x^2+256\cdot \:16[/tex]
[tex]=x^6-16x^4-256x^2+4096[/tex]
We can see that first term is x^6.
But for (x - 4)^8 expression, first term should be x^8.
So, we could say that Angela’s solution is incorrect.
