Introduction to Factorisation

Factorize the following polynomial: $32{\mathrm{x}}^4-500\mathrm{x}$.

Find the error present in the given mathematical expression, substitute $x=-3$ in the given expression  $x^2+5x={\left(-3\right)}^2+5\left(-3\right)=-9-15=-24$, and correct that error.

Find the error present in the given mathematical expression, substitute $x=-3$ in the given expression  $x^2-5x+6={\left(-3\right)}^2-5\left(-3\right)+6=9-15+6=0$, and correct that error.

Find the error present in the given mathematical expression, substitute $x=-3$ in the given expression  $x^2+7x+12={\left(-3\right)}^2+7\left(-3\right)+12=9+4+12=25$, and correct that error.

Factorisation of $16p^4+168p^3-88p^2$ is $k{p}^2\left(4p-2\right)\left(p+11\right)$

Find the value of $x-y$.

Find the error present in the given mathematical expression ${\left(x+8\right)}^2=x^2-64$, and correct that error.

Find the error present in the given mathematical expression $\left(2a-3\right)\left(a+2\right)=2a^2-6$, and correct that error.

Find the error present in the given mathematical expression ${\left(2x\right)}^2=2x^2$, and correct that error.

Find the error present in the given mathematical expression $3\left(x-4\right)=3x-4$, and correct that error.

Find the error present in the given mathematical expression $5x^3÷5x^3=0$, and correct that error.

Find the error present in the given mathematical expression $\left(x-4\right)\left(x-2\right)=x^2-8$, and correct that error.

Find the error present in the given mathematical expression $\left(x+4\right)\left(x+2\right)=x^2+8$, and correct that error.

Find the error present in the given mathematical expression $\left(3a+4b\right)\left(a-b\right)=3a^2-4b^2$, and correct that error.

Find the error present in the given mathematical expression ${\left(x+7\right)}^2=x^2+49$, and correct that error.

Find the error present in the given mathematical expression ${\left(x-4\right)}^2=x^2-16$, and correct that error.

Find the error present in the given mathematical expression ${\left(2a+3\right)}^2=2a^2+6a+9$, and correct that error.

Find the error present in the given mathematical expression ${\left(2x\right)}^2+5x=4x+5x=9x$, and correct that error.

Find the error present in the given mathematical expression ${\left(3x\right)}^2+4x+7=3x^2+4x+7$, and correct that error.

Find the error present in the given mathematical expression $3x+2y=6xy$, and correct that error.