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Addition and Subtraction of Algebraic Expression

iii Simplify ...

Question

Question 84 (iii)

Simplify

${(\frac{7}{9} a + \frac{9}{7} b)}^{2} - a b$

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Solution

We have, ${(\frac{7}{9} a + \frac{9}{7} b)}^{2} - a b$
$= {(\frac{7}{9} a)}^{2} + {(\frac{9}{7} b)}^{2} + 2 \times \frac{7}{9} a \times \frac{9}{7} b - a b$ [using the identity, $(a + b)^{2} = a^{2} + b^{2} + 2 a b$ ]
$= \frac{49}{81} a^{2} + \frac{81}{49} b^{2} + 2 a b - a b = \frac{49}{81} a^{2} + a b + \frac{81}{49} b^{2}$

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Question 84 (ix)

Simplify

$(a - b) (a^{2} + b^{2} + a b) - (a + b) (a^{2} + b^{2} - a b)$

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Addition and Subtraction of Algebraic Expression

Standard VIII Mathematics

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