a)
x2+14+9x
= x2+2x+7x+14
= x(x+2)+7(x+2)
= (x+2)(x+7)
b)
-5x2+11x-2
= -5x2+x+10x-2
= -x(5x-1)+2(5x-1)
= (5x-1)(2-x)
c) x4+4y4
= x4+4x2y2+4y4-4x2y2
= (x2+2y2)2-4x2y2
= (x2+2y2- 2xy)(x2+2y2+2xy)
a) \(x^2+14+9x\)
\(=x^2+14+2x+7x\)
\(=\left(x^2+2x\right)+\left(7x+14\right)\)
\(=x\left(x+2\right)+7\left(x+2\right)\)
\(=\left(x+2\right)\left(x+7\right)\)
b) \(-5x^2+11x-2\)
\(=-5x^2+10x+x-2\)
\(=-\left(5x^2-10x\right)+\left(x-2\right)\)
\(=-5x\left(x-2\right)+\left(x-2\right)\)
\(=\left(x-2\right)\left(-5x+1\right)\)
c) \(x^4+4y^4\)
\(=x^4+4y^4+4x^2y^2-4x^2y^2\)
\(=\left[\left(x^2\right)^2+2.x^2.2y^2+\left(2y^2\right)^2\right]-4x^2y^2\)
\(=\left(x^2+2y^2\right)^2-\left(2xy\right)^2\)
\(=\left(x^2+2y^2-2xy\right)\left(x^2+2y^2+2xy\right)\)
