Question

a) (x-1) (x²+x+1) = x³-1

b) (x³+x²y+xy²+y³)(x-y)=x⁴-y⁴

Answer 1

a)\(VT=\left(x-1\right)\left(x^2+x+1\right)\)

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

\(=x^3-x^2+x^2-x+x-1\)

\(=x^3-1=VP\)

b)\(VT=\left(x^3+x^2y+xy^2+y^3\right)\left(x-y\right)\)

\(=x^3\left(x-y\right)+x^2y\left(x-y\right)+xy^2\left(x-y\right)+y^3\left(x-y\right)\)

\(=x^4-x^3y+x^3y-x^2y^2+x^2y^2-xy^3+xy^3-y^4\)

\(=x^4-y^4\)

Answer 2

a) VT= x( x²+x+1) - 1( x²+x+1)

= x³+x²+x- x²-x-1

= x³-1