Find the value of 2a2 − 3ab when a = −3 and b = 4.
- 2a2 = 2 × (−3)2 = 2 × 9 = 18
- 3ab = 3 × (−3) × 4 = −36
- 2a2 − 3ab = 18 − (−36) = 18 + 36 = 54
Answer: 54
Introduction to algebra
Maths · Algebra and graphs. The idea in plain words, the rules to remember, the mistake to avoid and a worked example, written and checked by Mega Lecture.
The idea
In algebra a letter stands for a number. The letter may be a number we do not know yet, or any number at all. An expression such as 3x + 2y has no equals sign. A formula such as v = u + at links one quantity to others.
To substitute means to replace each letter with its number and then work out the value. Follow the order of operations: brackets, then powers, then multiplying and dividing, then adding and subtracting.
Take great care with negative numbers. Always put a negative number in brackets when you substitute it. The square of a negative number is positive, and subtracting a negative number is the same as adding.
Rules to remember
- 3x means 3 × x, xy means x × y, and x/y means x ÷ y
- x2 means x × x; 3x2 means 3 × (x2), so square first, then multiply by 3
- (−a)2 = a2, for example (−4)2 = 16
- Subtracting a negative: p − (−q) = p + q
- negative × negative = positive; negative × positive = negative
- "4 less than n" is n − 4; "3 more than n" is n + 3; "twice n" is 2n
Common mistake
Students work out 3p2 with p = −2 as (3 × −2)2 = 36, or as −12. Square first, in brackets: 3 × (−2)2 = 3 × 4 = 12.
Worked example
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