Question 84 ivSimplify 3-4x-4-3y 2-2xy

We have, ( 3/4x 4/3y )^2+2xy = ( 3/4x )^2 + ( 4/3y )^2 2 ×3/4x ×4/3y + 2xy [using the identity, (a b)^2=a^2+b^2 2ab] =9/16x^2+16/9y^2 2xy+2xy=9/16x^2+16 ...

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Standard VIII

Mathematics

Simplification of Rational Algebraic Expression

Question 84 i...

Question

Question 84 (iv)

Simplify

${(\frac{3}{4} x - \frac{4}{3} y)}^{2} + 2 x y$

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Solution

We have,
${(\frac{3}{4} x - \frac{4}{3} y)}^{2} + 2 x y = {(\frac{3}{4} x)}^{2} + {(\frac{4}{3} y)}^{2} - 2 \times \frac{3}{4} x \times \frac{4}{3} y + 2 x y$
[using the identity, $(a - b)^{2} = a^{2} + b^{2} - 2 a b$ ]
$= \frac{9}{16} x^{2} + \frac{16}{9} y^{2} - 2 x y + 2 x y = \frac{9}{16} x^{2} + \frac{16}{9} y^{2}$

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Simplification of Rational Algebraic Expression

Standard VIII Mathematics

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Question 84 (iv) Simplify (34x−43y)2+2xy

We have, (34x−43y)2+2xy=(34x)2+(43y)2−2×34x×43y+2xy [using the identity, (a−b)2=a2+b2−2ab] =916x2+169y2−2xy+2xy=916x2+169y2

Question 84 (iv)

Simplify

${(\frac{3}{4} x - \frac{4}{3} y)}^{2} + 2 x y$