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

Checking and securing understanding of expanding a single bracket

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 $$5(x + 7) + 3(4x + 5)$$ and simplify where possible.

Expand $$2(3x - 4) - 5(x - 6)$$ and simplify where possible.

Expand $$-4(x - 5) + 2(2x + 3)$$ and simplify where possible.

Expand $$3(x^2 - 2x) + 4(x - 3)$$ and simplify where possible.

Expand $$-2(x^2 + 3x) - 3(2x - 4)$$ and simplify where possible.

Expand $$4(2x - 3)^2 - 5(3x + 2)$$ and simplify where possible.

Evaluate the expression $$\frac{3x}{2x + 5}$$ for $$x = 3$$. Write your answer as a decimal.

Evaluate the expression $$\frac{x}{x + 1}$$ for $$x = 4$$. Write your answer as a decimal.

A company buys pencils in bulk for £2 per pen and sells them for £3.25 each. If the company sells $$x$$ pens, which of the following shows the correct expression for the profit, 'p'?

If a taxi charges a £15 base fare plus £2 per mile, which of the following represents the total cost, $$c$$, for a trip of $$x$$ miles?

A savings account offers 5% annual interest compounded yearly. If $$x$$ pounds are deposited, which expression represents the amount, $$a$$, in the account after one year?

A book store sells a book for £20, which is 20% more than its cost price. What is the cost price, 'p', of the book?

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