Algebra worksheet focusing on simplifying, expanding, and factorizing algebraic expressions.

Here are the solutions to the problems in the worksheet:

Section A: Simplify the expressions.

1. $a \times b = ab$
2. $3s \times 8t = 24st$
3. $x \times x = x^2$
4. $2y \times 4y = 8y^2$
5. $9pq \times p = 9p^2q$
6. $7cd \times 11d = 77cd^2$
7. $f \times f \times f = f^3$
8. $-4a \times 2 = -8a$
9. $12g \times -5g^2h = -60g^3h$
10. $-7k^2 \times -3k = 21k^3$

Section B: Expand the brackets.

1. $2(3x + 4) = 6x + 8$
2. $4(6y - 5) = 24y - 20$
3. $8(6 + 2t) = 48 + 16t$
4. $5x(y + 4) = 5xy + 20x$
5. $6a(3 - a) = 18a - 6a^2$
6. $7g(3g - 12) = 21g^2 - 84g$
7. $8u(5 - uv) = 40u - 8u^2v$
8. $3e(4ef - 6e) = 12e^2f - 18e^2$
9. $-4(7h - k) = -28h + 4k$
10. $-3d(a + 2b - 9d) = -3ad - 6bd + 27d^2$

Section C: Expand and simplify the expressions.

1. $8(6 + 3p) + 5p = 48 + 24p + 5p = 48 + 29p$
2. $3(x + 3) - 11 = 3x + 9 - 11 = 3x - 2$
3. $5 + 6(2s + 5) = 5 + 12s + 30 = 12s + 35$
4. $m + 7(6m - 4) = m + 42m - 28 = 43m - 28$
5. $4b + 2(2 - 5b) = 4b + 4 - 10b = -6b + 4$
6. $1 - 2(9w + 11) = 1 - 18w - 22 = -18w - 21$
7. $2n - 10(2 - 6n) + 25n = 2n - 20 + 60n + 25n = 87n - 20$
8. $5(9y + 8) + 2(3 - y) = 45y + 40 + 6 - 2y = 43y + 46$
9. $4(2j + 4) - (12 - j) = 8j + 16 - 12 + j = 9j + 4$
10. $8x(2 + 3x) - 2x(3 + x) = 16x + 24x^2 - 6x - 2x^2 = 22x^2 + 10x$

Section D: Factorise the following expressions.

1. $3h - 9 = 3(h - 3)$
2. $15w + 25 = 5(3w + 5)$
3. $16 - 22n = 2(8 - 11n)$
4. $ab + a = a(b + 1)$
5. $9jk + 21k = 3k(3j + 7)$
6. $12h - 16gh = 4h(3 - 4g)$
7. $2x^2 - x = x(2x - 1)$
8. $24c^2d + 32c^2 = 8c^2(3d + 4)$
9. $12q + 8p - 24 = 4(3q + 2p - 6)$
10. $6mn - 27m^2 + 9m = 3m(2n - 9m + 3)$