$Simplify (7 x + 4 y)^{2} + (7 x - 4 y)^{2}$

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Solution

To solve this, we need to use the following algebraic identities:

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

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

Adding the above two formulas we have:

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

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

Here we have a = 7x and b = 4y. Substituting this in the above expression we have:

$(7 x + 4 y)^{2} + (7 x - 4 y)^{2} = 2 (7 x)^{2} + 2 (4 y)^{2}$

$= 98 x^{2} + 32 y^{2}$

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Similar questions

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