Question

A= x^2- 4y^4, B= 8x^3+1 , C=54x^3-16y^3, D=x^2-6x+8, E=2x^2-5x+2, G=x^4+2x^2-3

Answer 1

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

\(B=8x^3+1=\left(2x+1\right)\left(4x^2-2x+1\right)\)

\(C=54x^3-16y^3=2\left(27x^3-8y^3\right)=2\left(3x-2y\right)\left(9x^2+6xy+4y^2\right)\)

\(D=x^2-6x+8=\left(x^2-6x+9\right)-1=\left(x-3\right)^2-1=\left(x-3-1\right)\left(x-3+1\right)=\left(x-4\right)\left(x-2\right)\)

\(E=2x^2-5x+2=\left(2x^2-4x\right)-\left(x-2\right)=2x\left(x-2\right)-\left(x-2\right)=\left(x-2\right)\left(2x-1\right)\)

\(G=x^4+2x^2-3=\left(x^4+3x^2\right)-\left(x^2+3\right)=x^2\left(x^2+3\right)-\left(x^2+3\right)=\left(x^2+3\right)\left(x^2-1\right)=\left(x^2+3\right)\left(x-1\right)\left(x+1\right)\)