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Question

Simplify (7x+4y)2+(7x4y)2

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Solution

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

(a+b)2=a2+2ab+b2

(ab)2=a22ab+b2

Adding the above two formulas we have:

(a+b)2+(ab)2=a2+2ab+b2+a22ab+b2

(a+b)2+(ab)2=2a2+2b2

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

(7x+4y)2+(7x4y)2=2(7x)2+2(4y)2

=98x2+32y2

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