[3 marks sum]

Question 513 Marks

Factorise the following by taking out the common factors:$(a - b)^2 -2(a - b)$

Answer

$(a-b)^2-2(a-b)$
Here, the common factor is ( $a-b)$.
Dividing throughout by ( $a-b)$,
we get
$\frac{(a-b)^2}{a-b}-\frac{2(a-b)}{a-b} $
$= a-b-2 $
$\therefore(a-b)^2-2(a-b) $
$=(a-b)(a-b-2) .$

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Question 523 Marks

Factorise the following by taking out the common factors:$24m^4n^6 + 56m^6n^4 - 72m^2n^2$

Answer

$24 m^4 n^6+56 m^6 n^4-72 m^2 n^2$
Here, the common factor is $8 m ^2 n ^2$
Dividing throughout by $3 a$,
we get
$\frac{24 m^4 n^6}{8 m^2 n^2}+\frac{56 m 6 n}{8 m^2 n^2}-\frac{72 m^2 n^2}{8 m^2 n^2} $
$=3 m^2 n^4+7 m^4 n^2-9 $
$\therefore 24 m^4 n^6+56 m^6 n^4-72 m^2 n^2 $
$=8 m^2 n^2\left(3 m^2 n^4+7 m^4 n^2-9\right) .$

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Question 533 Marks

Factorise the following by taking out the common factors:$12a^3+ 15a^2b - 21ab^2$

Answer

$12 a^3+15 a^2 b-21 a b^2$
Here, the common factor is $3 a$.
Dividing throughout by $3 a$, we get
$\frac{12 a^3}{3 a}+\frac{15 a^2 b}{3 a}-\frac{21 a b^2}{3 a} $
$=4 a^2+5 a b-7 b^2 $
$\therefore 12 a^3+15 a^2 b-21 a b^2 $
$=3 a\left(4 a^2+5 a b-7 b^2\right) .$

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Question 543 Marks

Factorise the following by taking out the common factors:$2x^5y + 8x^3y^2 - 12x^2y^3$

Answer

$2 x^5 y+8 x^3 y^2-12 x^2 y^3$
Here, the common factor is $2 x^2 y$.
Dividing throughout by $2 x^2 y$, we get
$\frac{2 x^5 y}{2 x^2 y}+\frac{8 X^3 y^2}{2 x^2 y}-\frac{12 x^2 y^3}{2 x^2 y} $
$=x^3+4 x y-6 y^2 $
$\therefore 2 x^5 y+8 x^3 y^2-12 x^2 y^3 $
$=2 x^2 y\left(x^3+4 x y-6 y^2\right) .$

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Question 553 Marks

Factorise the following by taking out the common factors:$5a(x^2 - y^2) + 35b(x^2 - y^2)$

Answer

$5 a\left(x^2-y^2\right)+35 b\left(x^2-y^2\right)$
Here, the common factor is $5\left(x^2-y^2\right)$.
Dividing throughout by $5\left(x^2-y^2\right)$.
we get
$\frac{5 a\left(x^2-y^2\right)}{5\left(x^2-y^2\right)}+\frac{35 b\left(x^2-y^2\right)}{5\left(x^2-y^2\right)} $
$=a+7 b $
$\therefore 5 a\left(x^2-y^2\right)+35 b\left(x^2-y^2\right) $
$=5\left(x^2-y^2\right)(a+7 b) .$

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Question 563 Marks

Factorise the following by taking out the common factors:$4x^2y^3 - 6x^3y^2 - 12xy^2$

Answer

$4 x^2 y^3-6 x^3 y^2-12 x y^2$
Here, the common factor is $2 x y^2$.
Dividing throughout by $2 x y^2$, we get
$\frac{4 x^2 y^3}{2 x y^2}-\frac{6 x^3 y^2}{2 x y^2}-\frac{12 x y^2}{2 x y^2} $
$=2 x y-3 x^2-6 $
$\therefore 4 x^2 y^2-6 x^3 y^2-12 x y^2 $
$=2 x y^2\left[2 x y-3 x^2-6\right] .$

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MATHEMATICS [3 marks sum]