Which of the following identity is not applicable to simplify 4 x -5 y 2-5 x -4 y 2 -A- a2-b2-a-ba-bB- a-b2-a2-2 ab -b2C- a-b2-a2-2 a b-b2D- Both A and B

The correct option is C = 2ab + (4x + 5y)^2 = (4x)^2 + 2 × (4x) × (5y) × (5y)^2 Using the identity, (a+b)^2 = a^2 + 2ab + b^2 (4x + 5y)^2 = 16x^2 + 40xy ...

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Byju's Answer

Standard VIII

Mathematics

Product of (x+y) (x-y)

Which of the ...

Question

Which of the following identity is not applicable to simplify ${(4 x + 5 y)}^{2} - {(5 x + 4 y)}^{2}$ ?

= + 2ab +

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- = (a + b)(a - b)

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= - 2ab +

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Both A and B

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Solution

The correct option is C
= - 2ab +

${(4 x + 5 y)}^{2} = {(4 x)}^{2} + 2 \times (4 x) \times (5 y) \times (5 y)^{2}$
Using the identity, ${(a + b)}^{2} = a^{2} + 2 a b + b^{2}$
${(4 x + 5 y)}^{2} = 16 x^{2} + 40 x y + 25 y^{2}$
${(5 x + 4 y)}^{2} = 25 x^{2} + 40 x y + 16 y^{2}$
Now, ${(4 x + 5 y)}^{2} - {(5 x + 4 y)}^{2} = (16 x^{2} + 40 x y + 25 y^{2}) - (25 x^{2} + 40 x y + 16 y^{2})$
$= 16 x^{2} + 40 x y + 25 y^{2} - 25 x^{2} - 40 x y - 16 y^{2}$
$= 9 y^{2} - 9 x^{2}$
OR
Using the identity, $a^{2} - b^{2} = (a + b) (a - b)$
${(4 x - 5 y)}^{2} - {(5 x + 4 y)}^{2} = [(4 x + 5 y) - (5 x + 4 y)] \times [(4 x + 5 y) + (5 x + 4 y)]$
$= (y - x) (9 x + 9 y)$
$= 9 x y - 9 x^{2} + 9 y^{2} - 9 x y$
$= 9 y^{2} - 9 x^{2}$

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Which of the following identity is not applicable to simplify (4x+5y)2−(5x+4y)2?

Which of the following identity is not applicable to simplify ${(4 x + 5 y)}^{2} - {(5 x + 4 y)}^{2}$ ?