$(4 x + 3 y)^{2} + (4 x - 3 y)^{2}$ is equal to

16 x^{2} - 9 y^{2}

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32 x^{2} + 18 y^{2}

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16 x^{2} + 9 y^{2}

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32 x^{2} + 9 y^{2}

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Solution

The correct option is B $32 x^{2} + 18 y^{2}$
Since, $(a + b)^{2} = a^{2} + b^{2} + 2 a b$ and $(a - b)^{2} = a^{2} + b^{2} - 2 a b$
$\Rightarrow (4 x + 3 y)^{2} + (4 x - 3 y)^{2} = (4 x)^{2} + (3 y)^{2} + 2 (4 x) (3 y) + (4 x)^{2} + (3 y)^{2} - 2 (4 x) (3 y)$
$= 2 (4 x)^{2} + 2 (3 y)^{2}$
$= 32 x^{2} + 18 y^{2}$
Option B is correct.

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(4x+3y)2+(4x−3y)2 is equal to

The correct option is B 32x2+18y2Since, (a+b)2=a2+b2+2ab and (a−b)2=a2+b2−2ab ⇒(4x+3y)2+(4x−3y)2=(4x)2+(3y)2+2(4x)(3y)+(4x)2+(3y)2−2(4x)(3y) =2(4x)2+2(3y)2 =32x2+18y2 Option B is correct.

$(4 x + 3 y)^{2} + (4 x - 3 y)^{2}$ is equal to