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Fundamental Concepts (Including Fundamental Operations) — MATHS STD 7 — Question

ICSE BoardEnglish MediumSTD 7MATHSFundamental Concepts (Including Fundamental Operations)2 Marks
Question
Evaluate: $\left(\frac{1}{2} a+\frac{1}{2} b\right)\left(\frac{1}{2} a-\frac{1}{2} b\right)$
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Answer


$\begin{aligned} & \left(\frac{1}{2} a+\frac{1}{2} b\right)\left(\frac{1}{2} a-\frac{1}{2} b\right) \\ & =\frac{1}{2 a}\left(\frac{1}{2} a-\frac{1}{2} b\right)+\frac{1}{2} b\left(\frac{1}{2} a-\frac{1}{2} b\right) \\ & =\frac{1}{4} a^2-\frac{1}{4} a b+\frac{1}{4} a b-\frac{1}{4} b^2 \\ & =\frac{1}{4} a^2-\frac{1}{4} b^2\end{aligned}$

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