Question

Представте выражение в виде произведения 1)с⁶-9х⁴;
2)х⁴у²-1;
3)25а²b²-16x⁴
4)100x²-y⁸

Answer 1

$1)c^6-9x^4=c^{2\times3}-3^2x^{2\times2}=(c^3)^2-3^2\times(x^2)^2=(c^3)^2-(3x^2)^2=(c^3-3^2)(c^3+3x^2)$

$2)x^4y^2-1=x^{2\times2}y^2-1^2=(x^2)^2\timesy^2-1^2=(x^2y)^2-1^2=(x^2y-1)(x^2y+1)$

$3)25a^2b^2-16x^4=5^2a^2b^2-4^2x^{2\times2}=(5ab)^2-4^2\times(x^2)^2=(5ab)^2-(4x^2)^2=(5ab-4x^2)(5ab+4x^2)$

$4)100x^2-y^8=10^2x^2-y^{2\times4}=(10x)^2-(y^4)^2=(10x-y^4)(10x+y^4)$