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.
This topic is about rewriting an expression in a different form without changing its value. You simplify by collecting like terms, which are terms with exactly the same letters and powers.
To expand means to multiply out brackets. Every term inside is multiplied by the term outside, and with two brackets every term in the first multiplies every term in the second. To factorise is the reverse: you put the brackets back. Always take out any common factor first, then look for a difference of two squares or a quadratic that splits into two brackets.
Completing the square rewrites a quadratic as a squared bracket plus or minus a number.
When a minus sign stands in front of a bracket, students change only the first sign, writing −(2a − 7b) as −2a − 7b. Every term inside the bracket changes sign, so it is −2a + 7b.
Answer: (3x + 2)(x − 4)
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