Question

(x +1)^2-5x(x+3)(x-3)

Answer 1

$\huge \boxed{\mathfrak{Question} \downarrow}$

• (x + 1)² - 5x (x + 3)(x - 3)

$\large \boxed{\mathfrak{Answer \: with \: Explanation} \downarrow}$

$( x + 1 ) ^ { 2 } - 5 x ( x + 3 ) ( x - 3 )$

Use binomial theorem $\left(a+b\right)^{2}=a^{2}+2ab+b^{2}$ to expand $\left(x+1\right)^{2}$.

$x^{2}+2x+1-5x\left(x+3\right)\left(x-3\right)$

Use the distributive property to multiply -5x by x+3.

$x^{2}+2x+1 + (-5x^{2}-15x)(x-3)$

Use the distributive property to multiply $-5x^{2}-15x$ by x-3 and combine like terms.

$x^{2}+2x+1-5x^{3}+45x$

Combine 2x and 45x to get 47x.

$\boxed{\boxed{\bf\:x^{2}+47x+1-5x^{3} }}$

OR

Follow the same steps till $x^{2}+2x+1-5x^{3}+45x$ and then use the algebraic identity ⇨ a + 2ab + b² = (a + b)²

$\boxed{\boxed{\bf\:-5x^{3}\left(x+1\right)^{2}+45x}}$