Factorise:
$(a + 2 b)^{2} + 101 (a + 2 b) + 100$

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Solution

$(a + 2 b)^{2} + 101 (a + 2 b) + 100 L e t a + 2 b = x \Rightarrow x^{2} + 101 x + 100 \Rightarrow x^{2} + (100 + 1) x + 100 \Rightarrow x^{2} + 100 x + x + 100 \Rightarrow x (x + 100) + 1 (x + 100) \Rightarrow (x + 100) (x + 1) putting the value of x \Rightarrow (a + 2 b + 100) (a + 2 b + 1)$

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