Question

Factorize:

1. x²+4x+4
2. x²-10x+25
3. a²+10ab+25b²
4.4x²+20xy+25y²
5. x⁴+6x²+9​

Answer 1

Step-by-step explanation:

(1)Rewrite it in the form $\sf{a}^{2}+2ab+{b}^{2}$, where a=x and b=2.

$\sf\red{{x}^{2}+2(x)(2)+{2}^{2}}$

$\sf\blue{\bullet}$ Use Square of Sum: $\sf{(a+b)}^{2}={a}^{2}+2ab+{b}^{2}$

.

$\sf\blue{\bullet{(x+2)}^{2}}$

(2)$\sf\blue{\bullet}$Rewrite it in the form $\sf{a}^{2}+2ab+{b}^{2}$, where a=x and b=5.

$\sf\red {\bullet \: {{x}^{2}+2(x)(5)+{5}^{2}}}$

$\sf\blue{\bullet}$Use Square of Sum: $\sf{(a+b)}^{2}={a}^{2}+2ab+{b}^{2}$

$\sf \orange{ \bullet \leadsto {(x + 5)}^{2} }$