Question 2(v)
Use the identity $(x + a) (x + b) = x^{2} + (a + b) x + a b$ to find the following products:
(2x+5y) ( 2x+3y)

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Solution

$(2 x + 5 y) (2 x + 3 y) = (2 x)^{2} + (5 y + 3 y) \times 2 x + 5 y \times 3 y$
$= 4 x^{2} + 8 y \times 2 x + 15 y^{2}$ $[U s i n g i d e n t i t y (x + a) (x + b) = x^{2} + (a + b) x + a b]$
$= 4 x^{2} + 16 x y + 15 y^{2}$

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(x + a) (x + b) = x^{2} + (a + b) x + a b

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Question 2(iv)
Use the identity $(x + a) (x + b) = x^{2} + (a + b) x + a b$ to find the following products:
$(4 x + 5) (4 x - 1)$

x^{2} + (a + b) x + a b .

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