#### Grouping to find a common factor - answers.

1.
ac + ad + bc + bd = (ac + ad) + (bc + bd)
2.
ac + ad - bc - bd = (ac + ad) - (bc + bd)

= (a + b)(c + d)

= (a - b)(c + d)
3.
(m - n)(p - q)
4.
(a + 1)(c + d)
5.
(x - 2)(m + n)
6.
(m + 2n)(x - 3)
7.
(a + 2b)(3c + d)
8.
(2a - b)(c - 3d)
9.
(x + 2y)(3x - 4z)
10.
(2x -y)(y + 5z)
11.
(a + 2)(b + 3)
12.
(c - 4)(d - 7)
13.
(m + 1)(n - 3)
14.
(p - 5)(q + 2)
15.
(2x + 3)(7 - 3y)
16.
(4 - 3x)(5 + 2y)
17.
2(a + 2)(b - 3)
18.
3(p + 3)(2q - 5)
19.
2(a + 2b)(3c - 4d)
20.
3(p + 2q)(2p + r)
21.
a(2a + b)(c - 3d)
22.
m(m - 2n)(p + 5q)
23.
2a(3a + b)(2c - 5d)
24.
3x(2x - 3y)(y + 2z)
25.
2a + 2b + ax + bx + ay + by = 2(a + b) + x(a + b) + y(a + b)
= (a + b)(2 + x + y)
26.
ap + bp + aq + bq + ar + br = p(a + b) + q(a + b) + r(a + b)
= (a + b)(p + q + r)
27.
(p - q)(x - y + z)(p - q)(x - y + z)
28.
(p - q)(a - b - c)
29.
(3x - y)(2m - n - 5p)
30.
3(2a + 3b)(x - y + 4z)

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