Question

Factorise 

1. \(x^ 2 + xy + 8x + 8y\)
2.  \(15xy - 6x + 5y - 2 \)
3.  \(ax + bx - ay - by\) 
4.  \(15pq + 15 + 9q + 25p\) 
5.  \(z - 7 + 7xy - xyz\)

Answer 1

(i) \(x^2 + xy + 8x + 8y = x \times x + x \times y + 8 \times x + 8 \times y\)
= \(x (x + y) + 8 (x + y)\)
= \((x + y) (x + 8)\)

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(ii) \(15xy - 6x + 5y - 2 = 3 \times 5 \times x \times y - 3 \times 2 \times x + 5 \times y - 2 \)
= \(3x \;(5y - 2) + 1 (5y - 2)\)
= \((5y - 2) (3x + 1)\)

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(iii) \(ax + bx - ay - by = a \times x + b \times x - a \times y - b \times y\)
= \(x (a + b) - y (a + b)\)
= \((a + b) (x - y)\)

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(iv) \(15pq + 15 + 9q + 25p = 15pq + 9q + 25p + 15\)
= \(3 \times 5 \times p \times q + 3 \times 3 \times q + 5 \times 5 \times p + 3 \times 5\)
= \(3q (5p + 3) + 5 (5p + 3)\)
= \((5p + 3) (3q + 5)\)

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(v) \(z - 7 + 7xy - xyz = z - x \times y \times z - 7 + 7 \times x \times y\)
= \(z (1 - xy) - 7 (1 - xy)\)
= \((1 - xy) (z - 7)\)