CameraIcon

SearchIcon

MyQuestionIcon

1

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Factorisation by Regrouping Terms

Resolve each ...

Question

Resolve each of the following quadratic trinomial into factor:
(2a − b)² + 2(2a − b) − 8

Open in App

Solution

$A s s u m i n g x = 2 a - b, w e h a v e : (2 a - b)^{2} + 2 (2 a - b) - 8 = x^{2} + 2 x - 8 T h e g i v e n e x p r e s s i o n b e c o m e s x^{2} + 2 x - 8 . (C o e f f i c i e n t o f x^{2} = 1 a n d t h a t o f x = 2; c o n s t a n t t e r m = - 8) N o w, w e w i l l s p l i t t h e c o e f f i c i e n t o f x i n t o t w o p a r t s s u c h t h a t t h e i r s u m i s 2 a n d t h e i r p r o d u c t e q u a l s t h e p r o d u c t o f t h e c o e f f i c i e n t o f x^{2} a n d t h e c o n s \tan t t e r m, i . e ., 1 \times (- 8) = - 8 . C l e a r l y, (- 2) + 4 = 2 a n d (- 2) \times 4 = - 8 R e p l a c i n g t h e m i d d l e t e r m 2 x b y - 2 x + 4 x, w e g e t : x^{2} + 2 x - 8 = x^{2} - 2 x + 4 x - 8 = (x^{2} - 2 x) + (4 x - 8) = x (x - 2) + 4 (x - 2) = (x + 4) (x - 2) R e l a c i n g x b y 2 a - b, w e g e t : (x + 4) (x - 2) = (2 a - b + 4) (2 a - b - 2)$

Suggest Corrections

thumbs-up

0

Similar questions

Q. Resolve each of the following quadratic trinomial into factor:
3 + 23y − 8y²

Q. Resolve each of the following quadratic trinomial into factor:
3x² + 22x + 35

Q. Resolve each of the following quadratic trinomial into factor:
14x² + 11xy − 15y²

Q. Resolve each of the following quadratic trinomial into factor:
6a² + 17ab − 3b²

Q. Resolve each of the following quadratic trinomial into factor:
15x² − 16xyz − 15y²z²

View More

Join BYJU'S Learning Program

similar_icon

Related Videos

lock

Method of Common Factors

MATHEMATICS

Watch in App

explore_more_icon

Explore more

Factorisation by Regrouping Terms

Standard VIII Mathematics

Join BYJU'S Learning Program

CrossIcon