Simplify using identity : (x + 4) (x – 3) (x – 5)
Answers
Given :- Simplify using identity : (x + 4) (x – 3) (x – 5)
Answer :-
→ (x + 4)(x - 3)( x - 5)
→ (x + 4){x - 3)(x - 5)}
using (x-a)(x-b) = x^2 - x(b+a) - ab
→ (x + 4)(x² - x(3 + 5) - 15)
→ (x + 4)(x² - 8x - 15)
→ x(x² - 8x - 15) + 4(x² - 8x - 15)
→ x³ - 8x² - 15x + 4x² - 32x - 60
→ x³ - 4x² - 47x - 60 (Ans.)
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JEE mains Question :-
https://brainly.in/question/22246812
Given : (x + 4) (x – 3) (x – 5)
To Find : Simplify using identity
Solution:
(x + 4)(x - 3)(x - 5)
= (x + 4)(x - 4+ 1)(x - 4-1)
= (x + 4)( (x - 4) + 1) ( (x - 4) - 1)
Apply identity (a + b)(a - b) = a² - b²
a = x - 4 , b = 1
= (x + 4 ) {( x - 4)² - 1 }
Using identity ( a - b)² = a² - 2ab + b²
= (x + 4 ) {x² -8x + 16 - 1 }
= (x + 4 ) {x² - 8x + 15 }
Using distributive property
= x({x² - 8x + 15 } + 4{x² - 8x + 15 }
= x³ - 8x² + 15x + 4x² - 32x + 60
= x³ - 4x² - 17x + 60
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