Question

Simplify using identity : (x + 4) (x – 3) (x – 5)

Answer 1

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

Answer 2

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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