Factorization a2+2ab+b2=(a+b)2

Factorization

a2+2ab+b2=(a+b)2

Example 1

$$\textup{Factorize } x^2+8x+16 $$

Solution

\begin{align*} &\because\;\; a^2+2ab+b^2=(a+b)^2 \\\\ &\therefore\;\; x^2+8x+16 \\ &=(x)^2+2(x)(4)+(4)^2 \\ &=(x+4)^2 \\ \end{align*}

Example 2

$$\textup{Factorize } y^2+6y+9 $$

Solution

\begin{align*} &\because\;\; a^2+2ab+b^2=(a+b)^2\\\\ &\therefore\;\; y^2+6y+9 \\ &=(y)^2+2(y)(3)+(3)^2 \\ &=(y+3)^2 \\ \end{align*}

Example 3

$$\textup{Factorize } 25x^2+20x+4 $$

Solution

\begin{align*} &\because\;\; a^2+2ab+b^2=(a+b)^2\\\\ &\therefore\;\; 25x^2+20x+4 \\ &=(5x)^2+2(5x)(2)+(2)^2 \\ &=(5x+2)^2 \\ \end{align*}

Example 4

$$\textup{Factorize } 16x^2+24x+9 $$

Solution

\begin{align*} &\because\;\; a^2+2ab+b^2=(a+b)^2\\\\ &\therefore\;\; 16x^2+24x+9 \\ &=(4x)^2+2(4x)(3)+(3)^2 \\ &=(4x+3)^2 \\ \end{align*}