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9.3 Substituting into expressions

9.3 Substituting into expressions

When you substitute numbers into expressions, remember BIDMAS.
Examples of indices are.
You must work out Brackets and Indices before Divisions and 4 , 7 , (−2) and (−3) 3
3
2
2
Multiplications.
You always work out Additions and Subtractions last.
Worked example 9.3

a Work out the value of the expression 5a − 6b when a = 4 and b = −3.
b Work out the value of the expression 3x − 2y when x = −5 and y = 2.
2
3
c Work out the value of the expression p(5 − 4q ) when p = 2 and q = −3.
p
a 5a − 6b = 5 × 4 − 6 × −3 Substitute a = 4 and b = −3 into the expression.
= 20 − −18 Work out the multiplications fi rst; 5 × 4 = 20 and 6 × −3 = −18
= 20 + 18 Subtracting −18 is the same as adding 18.
= 38
3
2
2
b 3x − 2y = 3 × (−5) − 2 × 2 Substitute x = −5 and y = 2 into the expression.
3
3
2
= 3 × 25 − 2 × 8 Work out the indices fi rst; (−5) = −5 × −5 = 25 and 2 = 2 × 2 × 2 = 8.
= 75 − 16 Then work out the multiplications; 3 × 25 = 75 and 2 × 8 = 16.
= 59 Finally work out the subtraction.
c p(5 − 4q ) = 2(5 − 4 ×− 3 ) Substitute p = 2 and q = −3 into the expression.
2
p
= 2(5 − −6) Work out the term in brackets fi rst. Start with the fraction.
4 × −3 = −12; −12 ÷ 2 = −6.
= 2 × (5 + 6) Subtracting −6 is the same as adding 6.
= 2 × 11 Finally, multiply the value of the term in brackets by 2; 2 × 11 = 22.
= 22
) Exercise 9.3

1 Work out the value of each expression when a = −2, b = 3, c = −4 and d = 6.
a b + d b a + 2b c 2d − b d a − c
e 4b + 2a f 3d − 6b g bd − 10 h d + ab
2
i d − a j 20 + b k ab + cd l bc + a
3
2 d
2 Work out the value of each expression when w = 5, x = 2, y = −8 and z = −1.
a 3(w + x) b x(2w − y) c x + yz d 3w − z 3
y
e x + y f (2x) g x − h wx + y
2
2
3
2 4 z
i 2(x − z ) j 25 − 2w k w + z(2x − y) l 2(w + x) − 3(w − x)
3
2
2
3 This is part of Dakarai’s homework.
Question Use a counter-example to show that
Use a counter-example to show that Question
2
2
these statements are not the statement 2x = (2x) is not
always true. always true.
2
2
Answer
2
a 3x = (3x) 2 Answer Let x = 3, so 2x = 2 × 3 = 2 × 9 = 18
2
2
2
b (−y) = −y 2 and (2x) = (2 × 3) = 6 = 36
2
c 2(a + b) = 2a + b  VR x  x) 2
2
88 9 Expressions and formulae