Algebra

NZ Level 6 (NZC) Level 1 (NCEA)

Expand further algebraic expressions

Lesson

We've learnt a number of techniques for expanding and simplifying algebraic expressions. Being familiar with the addition, subtraction, multiplication and division of algebraic terms, and having experience in expanding binomials, perfect squares and expressions resulting in the difference of two squares, means we can begin to work with some more complicated expressions.

Expand the following and simplify: $3u\left(3u-3v\right)$3`u`(3`u`−3`v`)

Expand and simplify the following:

$\left(5m+8\right)\left(m-3\right)$(5`m`+8)(`m`−3)

Expand and simplify the following expression $\left(x+7\right)\left(x-7\right)-\left(x-3\right)^2$(`x`+7)(`x`−7)−(`x`−3)2

Form and solve linear equations and inequations, quadratic and simple exponential equations, and simultaneous equations with two unknowns

Generalise the properties of operations with rational numbers, including the properties of exponents

Apply algebraic procedures in solving problems