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Factorisation Using Algebraic Identities

Factorize 4...

Question

Factorize $4 x^{2} + 12 x y + 9 y^{2}$

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Solution

Given $4 x^{2} + 12 x y + 9 y^{2}$
Since, we have $a^{2} + 2 a b + b^{2} = (a + b)^{2}$
Put $a = 2 x, b = 3 x$ in above formula, we get
$(2 x)^{2} + 2 (2 x) (3 y) + (3 y)^{2} = (2 x + 3 y)^{2}$
Thus, the factors of given expression are $(2 x + 3 y)^{2}$

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