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Students learn how to expand and factorise algebraic linear and quadratic expressions. Learning progresses to expanding cubic and factorising quadratics in the form ax^{2} +bx + c.

This unit takes place in Term 2 of Year 9 and is followed by solving equations.

Use and interpret algebraic notation, including:

- ab in place of a × b
- 3y in place of 3 × y
- a
^{2}in place of a × a, a^{3}in place of a × a × a and a^{2}b in place of a × a × b - a/b in place of a ÷ b
- Coefficients written as fractions rather than decimals

simplify and manipulate algebraic expressions by:

- Multiplying a single term over a bracket
- Taking out common factors
- Expanding products of two or more binomials
- Factorising quadratic expressions of the form (a)x
^{2}+ bx + c, including the difference of two squares - Simplifying expressions involving sums, products and powers including the laws of indices

- Students need to appreciate that writing with algebra applies the rules of arithmetic to unknown numbers which are represented as letters.
- It is important to define the difference between an expression, equation and formula.
- Linear (x), quadratic (x
^{2}) and cube terms (x^{3})cannot be collected together. - Understanding quadratics in the general form x
^{2}+ bx + c helps to factorise and expand expressions. - Developing mental methods to factorise quadratics is key to gaining confidence with quadratics equations later on.

- When multiplying out brackets students incorrectly forget to multiply the second term especially with negative products. E.g., 2(x + 5) = 2x + 10 and -2(x + 5) = -2x – 10
- When factorising expressions a common misconception is to not fully factorise. E.g., 18x + 24y can be written as 9x + 12y
- When expanding the product of two or more brackets students often incorrectly collect the like terms associated to the linear unknown

January 26, 2022

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