Question

Using the identity (x + a) (x + b) = x² + (a + b) x + ab to find the following products:-

1. (2p + 7) (2p - 5)
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Answer 1

Answer :-

$\\ \boxed{ \bold{(x + a)(x + b) = {x}^{2} + (a + b)x + ab }}$

here, in (2p + 7) (2p - 5)

• x = 2p
• a = 7
• b = -5

$\bold{: \implies {(2p)}^{2} + (7 - 5)2p + (7 \times - 5)} \\ \\ \bold{: \implies 4 {p}^{2} + 2(2p) - 35 } \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \bold{: \implies 4 {p}^{2} + 4p - 35 } \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

so, the answer is 4p² + 4p - 35

Answer 2

$1. (2p + 7) (2p - 5) \\ formula = (x + a) (x - b) = x² + (a - b) x + (a)(-b) \\ 2 {p}^{2} + (7 - 5)x + (7)( - 5) \\ 2 {p}^{2} + 7p - 5p - 35 \\ 2 {p}^{2} + 2p - 35 \: \: \: answer$