Factorize:
7(x-2y)²-25(x-2y)+12
Answers
Concept :
Here we factorise it by splitting the middle term.
- To factorise quadratic polynomials of the type ax² + bx + c by middle term splitting ,write b as the sum of two numbers whose product is ac.
- To factorise ax² + bx - c & ax²- bx - c , write b as the difference of two numbers whose product is - ac.
Given : 7(x - 2y)² - 25(x - 2y) + 12
Let a = (x – 2y)
Now we have,
= 7a² – 25a + 12
= 7a² – 21a – 4a + 12
= 7a(a - 3) -4 (a - 3)
= (7a – 4) (a - 3) …………(1)
On putting a = (x – 2y) eq 1:
= {7(x – 2y) – 4} (x – 2y - 3)
= (7x – 14y - 4) (x – 2y - 3)
7(x - 2y)² - 25(x - 2y) + 12 = (7x – 14y - 4) (x – 2y - 3)
Hence, the factorisation of 7(x - 2y)² - 25(x - 2y) + 12 is (7x – 14y - 4) (x – 2y - 3)
HOPE THIS ANSWER WILL HELP YOU…..
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Answer:
Step-by-step explanation:
Let a = (x – 2y)
Now we have,
= 7a² – 25a + 12
= 7a² – 21a – 4a + 12
= 7a(a - 3) -4 (a - 3)
= (7a – 4) (a - 3) …………(1)
On putting a = (x – 2y) eq 1:
= {7(x – 2y) – 4} (x – 2y - 3)
= (7x – 14y - 4) (x – 2y - 3)
7(x - 2y)² - 25(x - 2y) + 12 = (7x – 14y - 4) (x – 2y - 3)