question_answer

                                     

Factorise the following:

(a) \[\frac{{{x}^{2}}}{4}+2x+4\]

(b) \[16{{x}^{2}}+40x+25\]

Answer:

(a)   \[\frac{{{x}^{2}}}{4}+2x+4=\frac{1}{4}[{{x}^{2}}+8x+16]\]

\[=\frac{1}{4}[{{x}^{2}}+4x+4x+16]\]

\[=\frac{1}{4}[x(x+4)+4(x+4)]\]

\[=\frac{1}{4}[x(x+4)(x+4)]\]

\[=\frac{1}{4}{{(x+4)}^{2}}\]

(b)  \[163{{x}^{2}}+40x+25=16{{x}^{2}}+\left( 20+20 \right)x+25\]

\[=16{{x}^{2}}+20x+20x+25\]

\[=4x(4x+5)+5(4x+5)\]

\[=(4x+5)(4x+5)\]

\[={{(4x+5)}^{2}}\]