Use the identity $(x + a) (x + b) = x^{2} + (a + b) x + a b$ to find the following product:
(i) $(4 x - 5) (4 x - 1)$ (ii) $(4 x + 5) (4 x - 1)$

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Solution

$(i) (4 x - 5) (4 x - 1)$
$= (4 x)^{2} + 4 x (- 5 + (- 1)) + (- 5) (- 1)$
$= (4 x)^{2} + 4 x (- 6) + 5$
$= 16 x^{2} - 24 x + 5$
$(i i) (4 x + 5) (4 x - 1)$
$= (4 x)^{2} + 4 x (5 + (- 1)) + (5) (- 1)$
$= (4 x)^{2} + 4 x (4) - 5$
$= 16 x^{2} + 16 x - 5$

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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:
$(4 x + 5) (4 x - 1)$

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