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Question 73 Marks
Factorise : $5-\left(3 x^2-2 x\right)\left(6-3 x^2+2 x\right)$
Answer
$(1+3 x)(1-x)(1+x)(5-3 x)$
[Hint. Put $3 x^2-2 x=y$ ]
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Question 123 Marks
Factorise : $4(2 a-3)^2-3(2 a-3)(a-1)-7(a-1)^2 \quad$
Answer
$(a-5)(3 a-4)$
[Hint. Put $(2 a-3)=x$ and $(a-1)=y$.]
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Question 383 Marks
Factorise $\left(x^4+x^2 y^2+y^4\right)$
Answer
$\left(x^2+y^2+x y\right)\left(x^2+y^2-x y\right)$
[Hint. Given Exp. $=\left(x^4+2 x^2 y^2+y^4\right)-\left(x^2y^2\right)=\left(x^2+y^2\right)^2-(x y)^2$.
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Question 413 Marks
Express $\left(x^2+8 x-15\right)\left(x^2-8 x-15\right)$ as the difference of two squares.
Answer
$\left(x^2-15\right)^2-(8 x)^2$
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Question 423 Marks
Factorise : $9 a^2+3 a-8 b-64 b^2$
Answer
$(3 a-8 b)(3 a+8 b+1)$
[Hint. Given Exp. $=\left(9 a^2-64 b^2\right)+(3 a-8 b)$ ]
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Question 443 Marks
Factorise : $4 x^2-12 a x-y^2-z^2-2 y z+9 a^2$
Answer
$(2 x-3 a+y+z)(2 x-3 a-y-z)$
[Hint. Given Exp. $\left.=\left(4 x^2-12 a x+9 a^2\right)-\left(y^2+z^2+2 y z\right)\right]$
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Question 453 Marks
Factorise : $\left(a^2-b^2\right)\left(c^2-d^2\right)-4 a b c d$
Answer
$(a c-b d+a d+b c)(a c-b d-a d-b c)$
[Hint. Given Exp. $\left.=(a c-b d)^2-(a d+b c)^2\right]$
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Question 473 Marks
Factorise : $x^4+5 x^2+9$
Answer
$\left(x^2+3+x\right)\left(x^2+3-x\right) 2$
[Hint. Add and subtract $x^2$ ]
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Question 483 Marks
Factorise : $x^2+\frac{1}{x^2}-11$
Answer
$\left(x-\frac{1}{x}+3\right)\left(x-\frac{1}{x}-3\right)$
[Hint. Given Exp. $=\left(x^2+\frac{1}{x^2}-2\right)-9$ ]
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[3 marks sum] - MATHEMATICS STD 9 Questions - Vidyadip