A binomial is an algebraic expression representing the sum or difference of exactly 2 unlike terms.

The distributive law says that multiplying a sum is the same as multiplying each addend and summing the result.

The product of three binomials

Maths

In this unit, pupils learnt to solve quadratic equations by factorising and this skill will be required in the future unit through manipulating two simultaneous equations to find the solutions. For pupils studying the higher content, solving quadratic equations is required if one of the simultaneous equations is a quadratic.

In the prior unit, pupils used the distributive law to find the product of two binomials. In algebraic manipulation, pupils use apply this knowledge in order to factorise quadratics.

Algebraic manipulation

Expand and simplify the expression: $$(x + 2)(x - 3)(x + 4)$$

Expand and simplify the expression: $$(2x - 1)(x + 5)(3x - 2)$$

Expand and simplify the expression: $$(y - 2)(2y + 3)(y - 4)$$

Expand and simplify the expression: $$(3x + 1)(x - 2)(4x + 5)$$

Expand and simplify the expression: $$(2y - 3)(y + 4)(y - 5)$$

Expand and simplify the expression: $$(2x + 1)(3x - 2)(x - 4)$$

Make $$x$$ the subject of $$4x - 3y = 12$$

Make $$p$$ the subject of $$\frac{p}{2} + q = 7$$

Make $$a$$ the subject of $$3a -\frac{b}{4} + 2 = 0$$

Expand and simplify the expression: $$(x + 3)(x - 2)$$

Expand and simplify the expression: $$2(x + 5)(x - 3)$$

Expand and simplify the expression: $$x(x+5)(x-2)$$

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