Question

Factorise :

`\sf{ {x}^(2) - 4x - 21 + 10y - {y}^(2) }`
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Answer 1

(x+y-7)(x-y+3) is your answer

Explanation:

x²-4x-21+10y-y²

x²-4x+2²-2²-21+10y-y²

(x-2)²-(y2-10y+25)

(x-2)²-(y-5)²

(x-2+y-5)+x-2-y+5)

(x+y-7)(x-y+3)

Answer 2

(x - y + 3)(x + y - 7)

Explanation:

x^2 - 4x - 21 + 10y - y^2

= x^2 - y^2 - 4x -21 + 10y

= (x - y)(x + y) - 4x + 10y - 21 Now -21 = + 3 * -7 and +3x - 7x =- 4x so we try:

= (x - y + 3)(x + y - 7)

- this expands to the original expression.