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podryga [215]
3 years ago
9

Factorise 3(x+2)^2-10(x+2)+3

Mathematics
1 answer:
Likurg_2 [28]3 years ago
3 0
The answer is (x - 1)(3x + 5)


Let's substitute (x + 2) with a:
3(x + 2)² - 10(x + 2) + 3 = 3a² - 10a + 3 =
                                      = 3a² - 9a - a + 3 = 
                                      = 3a * a - 3a *3 - (a - 3) = 
                                      = 3a(a - 3) - (a - 3) =
                                      = (a - 3)(3a - 1)

Now, substitute a with x + 2:
(a - 3)(3a - 1) = (x + 2 - 3)(3(x + 2) - 1) = 
                     = (x - 1)(3x + 6 - 1) =
                     = (x - 1)(3x + 5)
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