Expressions involve the use of letters to represent quantities that are variable (or unknown), an expression does not contain an equals sign, so the only activities that will be carried out on expressions are collecting like terms, simplifying expressions, substituting in known values, expanding and factorising.
(a) Find the values of the following expressions if x = 3 and y = 5.
(i)5x + 4y
5(3) + 4(5) = 15 + 20 = 35
(ii)x2 + y2
(3)2 + (5)2 = 9 + 25 = 34
(b)(i)Multiply 5(3a - 4b).
5(3a - 4b) = 5(3a) - 5(4b) = 15a - 20b
(ii)Multiply x(x - y) + y(x + y). Write the answer in its simplest form.
x(x - y) + y(x + y) = x(x) - y(x) + y(y)
= x2 - xy + xy + y2
= x2 + y2
(c)Factorise fully each of the following:
(i)4xy - 6x2y2
= 2xy(2 - 3xy)
(ii)2ax - ay + 2bx - by
a(2x - y) + b(2x - y)
(a + b)(2x - y)