1. Expand: |
|
(a) 10(x − 6) |
(d) 3(2p − 3q + 8r) |
(b) 4q(q + 2) |
(e) -y(4y + 3) |
(c) -4x(2y + 3) |
(f) a2b(2a − b) |
2. Expand and simplify: |
|
(a) 3(b + 4) + 2(b + 5) |
(d) 6x − 3(x − 4) + 4x |
(b) 4c − 6(2 + 3c) |
(e) -2a − a(b + 3) + 2a(b + 3) |
(c) 2(p + 6) + 3(p − 4) |
(f) -2(3 + n) − 4(2 − n) + 3(n + 4) |
3. Expand the following quadratics: |
|
(a) (x + 2)(x + 4) |
(e) (3x + 4)(2x − 3) |
(b) (p + 8)(p − 3) |
(f) (4v − 8)(5v + 6) |
(c) (s − 2)(s − 4) |
(g) (2 − 3c)(c + 4) |
(d) (2q − 6)(q − 6) |
(h) (7r + 3)(5r − 2) |
4. Expand (write the products as sums): |
|
(a) (8y + x)(4y + x) |
(d) (3x − 2)(4x + 1) |
(b) (2x − 3)(3x + 5) |
(e) 2(8 − 2q)(q + 3) |
(c) (10 − x)(6 − x) |
(f) 4(a + b)(c − d) |
5. Expand the following perfect squares: |
|
(a) (a + 3)2 |
(d) (5d + 8)2 |
(b) (b − 1)2 |
(e) (3f + 20)2 |
(c) (2c − 3)2 |
(f) 2(e − 8)2 |
6. Expand the following: |
|
(a) (a − 1)(a + 1) |
(d) (4d − 20)(4d + 20) |
(b) (b + 8)(b − 8) |
(e) (2d + 3)(2d − 3) |
(c) (5c − 0.6)(5c + 0.6) |
(f) (3f -2g)(3f + 2g) |
7. Expand and simplify: |
|
(a) 6a(a − 8) |
(d) (d − 3)(2d − 4) |
(b) 3(b + 4) − 2(b − 6) |
(e) (e + 2) 2 |
(c) (c + 6)(c − 6) |
(f) (5f − 2)(f + 2) |
8. Expand and simplify: |
|
(a) (a + 3)3 |
(d) (5d + 8)3 |
(b) (b − 1)3 |
(e) (3f + 20)(f − 2)(f + 5) |
(c) (c − 3)(c + 4)(c − 5) |
(f) 2(e + 4)(e − 8)2 |