Question

x⁴-y⁴
x²-3y²
9(x-y)²-4(x+y)²
(4x²-4x+1)-(x+1)²
x³+27
27x³-0.001
125x³-1

 

Answer 1

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

\(x^2-3y^2=\left(x-\sqrt{3}y\right)\left(x+\sqrt{3}y\right)\)

\(9\left(x-y\right)^2-4\left(x+y\right)^2=\left[3\left(x-y\right)\right]^2-\left[2\left(x+y\right)\right]^2=\left[3\left(x-y\right)-2\left(x+y\right)\right]\left[3\left(x-y\right)+2\left(x+y\right)\right]=\left(3x-3y-2x+2y\right)\left(3x-3y+2x+2y\right)=\left(x-y\right)\left(5x-y\right)\)

\(x^3+27=\left(x+3\right)\left(x^2-3x+9\right)\)

\(27x^3-0,001=\left(3x-0,1\right)\left(9x^2+0,3x+0,01\right)\)

\(125x^3-1=\left(5x-1\right)\left(25x^2+5x+1\right)\)

Answer 2

a: \(x^4-y^4=\left(x-y\right)\left(x+y\right)\left(x^2+y^2\right)\)

c: \(9\left(x-y\right)^2-4\left(x+y\right)^2=\left(3x-3y-2x-2y\right)\left(3x-3y+2x+2y\right)=\left(x-5y\right)\left(5x-y\right)\)

d: \(\left(4x^2-4x+1\right)-\left(x+1\right)^2=\left(2x-1\right)^2-\left(x+1\right)^2\)

\(=\left(2x-1-x-1\right)\left(2x-1+x+1\right)\)

\(=3x\left(x-2\right)\)

e: \(x^3+27=\left(x+3\right)\left(x^2+3x+9\right)\)