Question

ADUCETI EXPRESIILE DE MAI JOS LA O FORMA MAI SIMPLAA
$x^{3} -8=$
$x^{2} -81$=
$(3x+4y) ^{2} -(4x+3y) ^{2}$

Answer 1

a³ - b³ = ( a -b ) ( a² + ab + b²)
1) =(x-2)(x²+2x+4)

(a + b)  ( a - b ) = a² - b²
2)= (x+9)(x-9)=(x+9)(√x+3)(√x-3)

 ( a + b )² = a² + 2ab + b²    
3)=(9x²+24xy+16y²)-(16x²+24xy+9y²)=9x²+24xy+16y²-16x²-24xy-9y²=7y²-7x²=(√7y+√7x)(√7y-√7x)

Answer 2

1) x³-8=x³-2³=(x-2)(x-2)²=(x-2)(x²+2x+4)


2)x²-81=x²-9²= (x-9)(x+9)


3)(3x+4y)²-(4x+3y)²=(9x²+24xy+16y²)-(16x²+24xy+9y²)=9x²+24xy+16y²-16x²-24xy-9y²=7y²-7x²