Question

Factorise the expressions 

1.  \(ax^2 + bx\) 
2.  \(7p^ 2 + 21q^ 2\) 
3.  \(2x^ 3 + 2xy^2 + 2xz^2\) 
4.  \(am^2 + bm^2 + bn^2 + an^2\) 
5.  \((lm + l) + m + 1\) 
6.  \(y(y + z) + 9(y + z)\) 
7.  \(5y^ 2 - 20y - 8z + 2yz\) 
8.  \(10ab + 4a + 5b + 2\) 
9.  \(6xy - 4y + 6 - 9x\)

Answer 1

(i) \(ax^2 + bx = a \times x \times x + b  x\) 
= \( x(ax + b)\)

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(ii) \(7p^ 2 + 21q^ 2\) = \(7 \times p \times p + 3 \times 7 \times q \times q\) 
= \(7(p^ 2 + 3q ^2 )\)

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(iii) \(2x 3 + 2xy^2 + 2xz^2 = 2x(x^ 2 + y^ 2 + z ^2 )\)

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(iv) \(am^2 + bm^2 + bn^2 + an^2 = am^2 + bm^2 + an^2 + bn^2\) 
= \(m^2 (a + b) + n^ 2 (a + b)\) 
= \((a + b) (m^2 + n^ 2 )\)

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(v) \((lm + l) + m + 1 = lm + m + l + 1\) 
= \(m(l + 1) + 1(l + 1)\) 
= \((l + l) (m + 1)\)

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(vi) \(y (y + z) + 9 (y + z) = (y + z) (y + 9)\)

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(vii) \(5y^ 2 - 20y - 8z + 2yz = 5y ^2 - 20y + 2yz - 8z\) 
= \(5y(y - 4) + 2z(y - 4)\) 
=\( (y - 4) (5y + 2z)\)

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(viii) \(10ab + 4a + 5b + 2 = 10ab + 5b + 4a + 2\)
= \(5b\;(2a + 1) + 2\;(2a + 1)\) 
= \((2a + 1) (5b + 2)\)

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(ix) \(6xy - 4y + 6 - 9x = 6xy - 9x - 4y + 6\) 
= \(3x(2y - 3) - 2(2y - 3)\) 
= \((2y - 3) (3x - 2)\)