Question

factorise using suitable identies 1) x ² - 81 2) x ² - 5x - 24​

Answer 1

To factorise:

✰ x² - 81

✰ x² - 5x - 24

Step-by-step explanation:

1.

Difference of two squares:

Since, the product of ( x + y ) and ( x - y ) = ( x + y ) ( x - y ) = x² - y²

∴ Factors of x² - y² are ( x + y ) and ( x - y ),

that is, x² - y² = ( x + y ) ( x - y )

Therefore,

➛ x ² - 81

➛ x ² - 9²

✭ a² - b² = ( a + b ) ( a - b )

➛ ( x + 9 ) ( x - 9 ) Ans.

2.

When trinomial of the form ax² ± bx ± c ( By splitting the middle term )

When trinomial is of the form ax² + bx + c, split b, the middle term into two parts such that the sum of these two parts is equal to b and the product of these two parts is equal to product of a and c. Then factorise by grouping method.

➛ x² - 5x - 24

Since,

- 8 + 3 = - 5

( - 8 ) × 3 = - 24

➛ x² - 8x + 3x - 24

➛ x ( x - 8 ) +3 ( x - 8 )

➛ ( x - 8 ) ( x + 3 ) Ans.

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