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MATHS [5 marks sum]

Factorisation · ICSE STD 8 (ICSE - English Medium). 3 questions.

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3 questions · timed · auto-graded

Question 15 Marks
Factorise : $15(2x - y)^2 - 16(2x - y) - 15$
Answer
$15(2x - y)^2 - 16(2x - y) - 15=$  Let $2x - y = a,$ then
$15a^2 - 16a - 15$
$= 15a^2 - 25a + 9a - 15$
$...{15 \times (-15) = -225 , -225 = -25 \times 9 , -16 = -25 + 9}$
$= 5a (3a - 5) + 3(3a - 5)$
$= (3a - 5)(5a + 3)$
$= [3 (2x - y) - 5][5 (2x - y) + 3]$
$= (6x - 3y - 5)(10x - 5y + 3)$
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Question 25 Marks
Factorise : $x^4 - 5x^2 - 36$
Answer
$x^4 - 5x^2 - 36= (x^2)^2 - 5x^2 - 36$
$= (x^2)^2 - 9x^2 + 4x^2 - 36 ...{\because -36 = -9 \times 4 }$
${-5 = -9 + 4}$
$= x^2 (x^2 - 9) + (x^2 - 9)$
$= (x^2 - 9)(x^2 + 4)$
$= [x^2 - (3)^2] [x^2 + 4]$
$= (x + 3)(x - 3)(x^2 + 4)$
$= (x^2 +4) (x + 3)(x - 3)$
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Question 35 Marks
Factorise : $25(2x + y)^2 - 16(x - y)^2$
Answer
$25(2x + y)^2 - 16(x - y)^2$
$= [5(2x + y)]^2 - [4(x-y)]^2$
$= (10x + 5y)^2 - (4x - 4y)^2$
$= (10x + 5y + 4x - 4y) (10x + 5y - 4x + 4y)$
$= (14x + y)(6x + 9y)$
$= (14x + y) 3(2x + 3y)$
$= 3 (14x + y)(2x + 3y)$
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[5 marks sum] - MATHS STD 8 Questions - Vidyadip