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Algebraic Expressions and Identities — MATHS STD 8 — Question

Gujarat BoardEnglish MediumSTD 8MATHSAlgebraic Expressions and Identities1 Mark
Question
Write the following squares of binomials as trinomials:
$\big(\frac{2\text{a}}{3\text{b}}+\frac{2\text{b}}{3\text{a}}\big)^2$
✓

Answer

We will use the identities $(a+b)^2=a^2+2 a b+b^2$ and $(a-b)^2=a^2-2 a b+b^2$ to convert the squares of binomials as trinomials.
$\big(\frac{2\text{a}}{3\text{b}}+\frac{2\text{b}}{3\text{a}}\big)^2$
$=\big(\frac{2\text{a}}{3\text{b}}\big)^2+2\big(\frac{2\text{a}}{3\text{b}}\big)\big(\frac{2\text{b}}{3\text{a}}\big)+\big(\frac{2\text{b}}{3\text{a}}\big)^2$
$=\frac{4\text{a}^2}{9\text{b}^2}+\frac{8}{9}+\frac{4\text{b}^2}{9\text{a}^2}$

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