Mathematics
Simplify the following:
(x+2y+3)(x+2y+7)
Expansions
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Answer
(x+2y+3)(x+2y+7)
Let (x+2y)=z
Then the given expression = (z+3)(z+7)
We know that (x+a)(x+b) = x2 + (a + b)x + ab
∴ (z+3)(z+7) = z2 + (3+7)z + (3)(7)
= z2 + 10z + 21
= (x+2y)2 + 10(x+2y) + 21
= x2 + 2(x)(2y) + (2y)2 + 10x + 20y + 21
= x2 + 4xy + 4y2 + 10x + 20y + 21
= x2 + 10x + 4y2 + 20y + 4xy + 21
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