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Algebraic Expressions Expansion

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Algebraic Expressions Expansion

Expand by multiplying each term in one bracket by each term in the other. Collect like terms and show your working. When asked, factorise by taking out the highest common factor.

Expand, simplify and factorise

1.Use an area model to expand and simplify (x + 4)(x + 3). Label the four partial products.

Draw and label a 2 by 2 rectangle to show the products.

2.Expand (2x + 3)(x + 5) using an area model or distribution. Simplify your result.

Show the partial products or draw an area model.

3.Which property justifies multiplying every term in one bracket by every term in the other when expanding (a + b)(c + d)?

The commutative property
The associative property
The distributive property
The identity property

4.Expand and simplify (x + 6)(x − 2).

5.Complete the distribution: 4(x + 7) = 4 × + 4 × = .

6.Factorise 10x + 15 by taking out the highest common factor.

7.Factorise 6x² − 9x by taking out the highest common factor.

8.Which expressions are equivalent to 3x + 9? Select all that apply.

3(x + 3)
x + 3 + 2x + 6
3x + 3
(x + 9) + 2x

9.Match each expression on the left to its expanded or factorised equivalent on the right.

(x + 2)(x + 5)
(x − 3)(x + 4)
2(x + 6)
8x + 12
(x + 1)²

x² + x − 12
4(2x + 3)
2x + 12
x² + 2x + 1
x² + 7x + 10

10.Expand and simplify (x − 5)².

Apply and extend

11.A rectangular paddock has side lengths (x + 7) metres and (x + 2) metres. Write its area as a product, then expand and simplify the expression. Include square metres in your answer.

12.Expand and simplify (2x − 1)(x² + 3x + 4).

13.Explain why an area model can help when expanding two brackets. Include how the smaller areas relate to the terms in the expanded expression.