Question

Factorise each of the following.
(a) (2x + 1)² - 10(2x + 1) + 25
(b) 4(3t - 1)² – (7t + 5)²
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Answer 1

Answer:

a-

Step-by-step explanation:

(4x+1)- (20x+1)+25

Answer 2

(a) (2x + 1)² - 10(2x + 1) + 25

(2x)² + 2(2x)(1) + (1)² - 10(2x+1) + 25

4x² + 4x + 1 - 20x - 10 + 25

4x² -16x + 16

4[x² - (2+2)x + 4]

4[x(x-2) + 2(x-2)]

4[(x+2) (x-2)]

(b) 4(3t - 1)² – (7t + 5)²

4[(3t)² + (1)² - 2(3t)(1)] - (7t)² + 2(7t)(5) + (5)²

4[ 9t² + 1 - 6t ] - 49t² + 70t + 25

36t² + 4 - 24t - 49t² + 70t + 25

-13t² + 46t + 29

Used identities:-

(a+b)² = a²+ b² + 2ab

(a-b)² = a²+ b² - 2ab