Question

X^8 - 256

Answer 1

\(x^8-256\)

\(=\left(x^4\right)^2-16^2\)

Ta có:\(\left(a+b\right)\left(a-b\right)=a\left(a+b\right)-b\left(a+b\right)\)

\(=a^2+ab-ba-b^2\)

\(=a^2-b^2\)

Vậy \(a^2-b^2=\left(a+b\right)\left(a-b\right)\)

Áp dụng:\(\left(x^4\right)^2-16^2=\left(x^4+16\right)\left(x^4-16\right)\)

\(=\left(x^4+16\right)\left[\left(x^2\right)^2-4^2\right]\)

\(=\left(x^4+16\right)\left(x^2+4\right)\left(x^2-4\right)\)

\(=\left(x^4+16\right)\left(x^2+4\right)\left(x+2\right)\left(x-2\right)\)

Answer 2

= 4x⁸ - 3x⁸ - \(\sqrt{256}\)

= 4x⁸ - 3x⁸ - 16

= (4x⁸ - 16) - 3x⁸

= 4(x⁸ - 4) - 3x⁸

= bó tay!!

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Answer 3

\(x^8-256\)

\(=x^8-2^8\)

\(=\left(x-2\right)\left(x^7+2x^6+4x^5+8x^4+16x^3+32x^2+64x+128\right)\)