Question

Algebraic formulas of class 8


`{25x}^(2) - {36y}^(2)`

`{4x}^(2) + 12 + 9`
​

Answer 1

Solution :-

1) 25x² - 36y²

We know that it is in form of algebraic identities a² - b² = (a + b) (a - b)

So,

→ (5x)² - (6y)²

→ (5x + 6y ) (5x - 6y ) Ans .

`\underline{\rule {290pt } {4pt}}`

2) 4x² + 12 + 9

Correct Question -

• 4x² + 12x + 9

By Using middle term splitting method of factorisation,,

→ 4x² + 12x + 9

→ 4x² + 6x + 6x + 9

→ (4x²+ 6x ) + (6x +9)

→ 2x (2x + 3) + 3(2x + 3)

→ (2x + 3) (2x +3) Ans

Answer 2

(5x - 6y)(5x + 6y) , (2x + 3)²

Explanation:

assuming you require to factorise the expressions

25x² - 36y² ← is a difference of squares and factorises in general as

a² - b² = (a - b)(a + b) , so

25x² - 36y²

= (5x)² - (6y)² with a = 5x and b = 6y , then

25x² - 36y² = (5x - 6y)(5x + 6y) ← in factored form

------------------------------------------------

4x² + 12x + 9

consider the factors of the product of the coefficient of the x² term and the constant term which sum to give the coefficient of the x- term

product = 4 × 9 = 36 and sum = + 12

the factors are + 6 and + 6

use these factors to split the x- term

4x² + 6x + 6x + 9 ( factor the first/second and third/fourth terms )

= 2x(2x + 3) + 3(2x + 3) ← factor out (2x + 3) from each term

= (2x + 3)(2x + 3)

= (2x + 3)² ← in factored form