MA10-07 Maths Coming soon

Completing the Square

MA10-07

This lesson is coming soon.

Watch now instead: MA11-01 Solving Linear Equations by Balancing

In this lesson

Write a quadratic expression in completed-square form, including when the leading coefficient is not 1.

What it covers

Writing a quadratic expression x^2+bx+c in the form (x+p)^2+q
Extracting a leading coefficient a not equal to 1 before completing the square inside the bracket, then redistributing it correctly

Key words

completing the square completed square form

For: Eduqas GCSE C300, Edexcel IGCSE 4MA1, OCR GCSE J560, Cambridge IGCSE 0580

On the specification

Board	Spec	Statement
Eduqas GCSE C300	HA4	Simplify and manipulate algebraic expressions (including those involving surds and algebraic fractions) by: collecting like terms; multiplying a single term over a bracket; taking out common factors; expanding products of two or more binomials; factorising quadratic expressions of the form x² + bx + c, including the difference of two squares; factorising quadratic expressions of the form ax² + bx + c; completing the square; simplifying expressions involving sums, products and powers, including the laws of indices
Edexcel IGCSE 4MA1	H2.2D	Complete the square for a given quadratic expression
OCR GCSE J560	6.01f	Complete the square on a quadratic expression.
Cambridge IGCSE 0580	E2.2	Simplify expressions by collecting like terms.

For teachers

This GCSE Maths lesson teaches completing the square. By the end, students should be able to write a quadratic expression in completed-square form, including when the leading coefficient is not 1. It works through two worked examples and the mistakes examiners report.