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Polynomials — MATHS STD 9 — Question

Rajasthan BoardEnglish MediumSTD 9MATHSPolynomials1 Mark
Question
Using suitable identity Expand: $\left[\frac{1}{4} a-\frac{1}{2} b+1\right]^{2}$
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Answer

$\left[\frac{1}{4} a-\frac{1}{2} b+1\right]^{2}$
$= \left[\frac{1}{4} a+\left(-\frac{1}{2} b\right)+1\right]^{2}$
$($Using Identity $(a + b + c)^2= a^2+ b^2+ c^2+ 2ab + 2bc + 2ca)$
$= \left(\frac{1}{4} a\right)^{2}+\left(-\frac{1}{2} b\right)^{2}$ + $+(1)^{2}+2\left(\frac{1}{4} a\right)\left(-\frac{1}{2} b\right)+2\left(-\frac{1}{2} b\right)(1)+2(1)\left(\frac{1}{4} a\right)$
$= \frac{1}{16} a^{2}+\frac{1}{4} b^{2}+1-\frac{1}{4} a b-b+\frac{1}{2} a$

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