2.01 Factorise algebraic expressions
Find the highest common algebraic factor of the following terms:
9 x and 8 x
9 x n and 4 a x
18 b^{2} n and 7 b^{2} m
13 y^{2} a n and 17 m y^{2} b
9 b x m and 5 b x a
8 m y and 12 a m
15 n^{2} m and 8 n m^{2}
20 x and 15 x^{2} n
16 a b n x and 12 a b m y
6abmn and 8bnxy
16 a^{2} b x^{3} y^{6} and 12 b^{4} m^{2} n^{6} x
12a^7bm^3y^2 and 9ab^5n^2x^3
3 b x, 2 n b and 5 b a
4 x^{2} a n, 3 b x^{4} m and 12 m a x^{3}
Complete the following:
y^{2} + 5 y = y \left(⬚ + ⬚\right)
- m^{2} + 19 m = ⬚ \left(m - 19\right)
8 v - v^{2} = v \left(⬚\right)
11 u - 19 u^{2} = u \left(⬚ - ⬚\right)
- 38 x y - 4 y^{2} = ⬚ \left( 19 x + 2 y\right)
Factorise:
- 12 s + 10
- 35 m + 49 n
Factorise:
A student incorrectly used the distributive law and wrote -5x^3-15x=-5x\left(x^2-3\right).
Explain how to correct the error, and write the correct answer.
Find the highest common factor of the terms: 12 p^{2} r^{2} t^{3}, 9 p r t^{3}, and 18 p^{3} r^{3} t^{-2}.
12 x^{4} + 18 x^{3} - 24 x^{2} can be factorised into the form 6 x \left( 2 x^{3} + 3 x^{2} - 4 x\right). Has the expression been fully factorised? Explain your answer.