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Addition and Subtraction of Algebraic Expression

Simplify : ...

Question

Simplify : ${(4 m + 5 n)}^{2} - {(4 m - 5 n)}^{2}$

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Solution

${(4 m + 5 n)}^{2} - {(4 m - 5 n)}^{2}$ is of the form $a^{2} - b^{2} = (a + b) (a - b)$

where $a = 4 m + 5 n, b = 4 m - 5 n$

$= (4 m + 5 n + 4 m - 5 n) (4 m + 5 n - 4 m + 5 n)$

$= (8 m) (10 n)$

$= 80 m n$

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(4 m + 5 n)^{2} + (5 m + 4 n)^{2}

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Q. Simplify the following expression:

(4 m + 5 n)^{2} + (5 m + 4 n)^{2}

(4 m + 5 n)^{2} + (5 m + 4 n)^{2}

(4 m + 5 n)^{2} + (5 m + 4 n)^{2}

Simplify:
$(4 m + 5 n)^{2} + (5 m + 4 n)^{2}$

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