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