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Year 7 Interactive Maths - Second Edition


The Distributive Law

Consider the expression a(b + c).

This expression represents the area of a rectangle of length b + c and width a.  So, this expression can be represented as:

This drawing illustrates the Distributive Law.

This can be split up into two parts as follows:

This drawing illustrates the Distributive Law.

Now, the sum of the areas of the rectangles = ab + ac.

This suggests that:

a(b + c) = ab + ac

This is called the Distributive Law.


Example 14

Expand 7(x + 8) and 8(x + 6).

Solution:

Use the Distributive Law to expand the expression.

Use the Distributive Law to expand the expression.


Example 15

Expand 5(y - 9) and 8(x - 4).

Solution:

Use the Distributive Law to expand the expression.

Use the Distributive Law to expand the expression.


Example 16

Expand and simplify 5(3 - x) + 7(x + 3) and 4(x + 3) + 2(x - 4).

Solution:

Use the Distributive Law to expand the expression and then add like terms.

Use the Distributive Law to expand the expression and then add like terms.


Key Term

Distributive Law


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