Question

(x^2+2x+4)^2-5(x^4+4x^2+16)+(2x^2-4x+8)^2


(x^2+2x)(x^2+2x+3)+2

Answer 1

Explicație pas cu pas:

(x²+2x+4)²-5(x⁴+4x²+16)+(2x²-4x+8)²

=(x⁴+4x²+16+4x³+16x+8x²)-(5x⁴+20x⁴+90)+(4x²+16x²+64-16x³-64x+32x³)=

x⁴+12x²+16+4x³+16x-25x⁴-90+20x²+64+16x³-64x

=-24x⁴+32x²-74+20x³-48x=2(-12x⁴+16x²-37+10x³-24x)

(x²+2x)(x²+2x+3)+2=x³+2x³+3x²+2x³+4x²+6x+2=5x³+7x²+6x+2=x(5x²+7x+6)+2