Question

Factor this fully

4(x-2)^{2} -21(x-2)-25

Answer 1

Answer:

$(4x - 33)(x - 1)$

Step-by-step explanation:

$let \: x - 2 = y \\ \\ 4 {y}^{2} - 21y - 25 \\ \\ = > 4 {y}^{2} + 4y - 25y - 25 \\ \\ = > 4y(y + 1) - 25(y + 1) \\ \\ = > (4y - 25)(y + 1) \\ \\ put \: y = x - 2 \\ \\ = > (4(x - 2) - 25)(x - 2 + 1) \\ \\ = > (4x - 33)(x - 1)$

HOPE IT HELPS

Answer 2

Given :  4(x - 2)²  - 21(x - 2)  - 25

To find : Factorize

Solution:

4(x - 2)²  - 21(x - 2)  - 25

= 4(x - 2)²  + 4(x - 2) - 25(x - 2) - 25

= 4(x - 2)(x - 2 + 1) - 25(x - 2 + 1)

= ( 4x - 8 - 25)(x - 1)

= (4x - 33)(x - 1)

Another way

4(x - 2)²  - 21(x - 2)  - 25

= 4(x²  - 4x + 4) - 21x + 42 - 25

= 4x² - 16x + 16 - 21x + 17

= 4x² - 37x  + 33

= 4x² - 4x - 33x + 33

= 4x(x - 1) - 33(x - 1)

= (4x - 33)(x - 1)

4(x - 2)²  - 21(x - 2)  - 25 = (4x - 33)(x - 1)  

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