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) \[163{{x}^{2}}+40x+25=16{{x}^{2}}+\left( 20+20 \right)x+25\] \[=16{{x}^{2}}+20x+20x+25\] \[=4x(4x+5)+5(4x+5)\] \[=(4x+5)(4x+5)\] \[={{(4x+5)}^{2}}\]
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