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9.7 Expanding the product of two linear expressions

9.7 Expanding the product of two linear expressions

When you multiply two expressions in brackets together, you must multiply each term in the #rst pair
of brackets by each term in the second pair of brackets.

Worked example 9.7

Expand and simplify these expressions. a (x + 2)(x + 3) b (y + 8)(y − 4)

a (x + 2)(x + 3) First, multiply the x in the first brackets by the x in the second brackets to give x .
2
Then, multiply the x in the first brackets by the 3 in the second brackets to give 3x.
Then, multiply the 2 in the first brackets by the x in the second brackets to give 2x.
Finally, multiply the 2 in the first brackets by the 3 in the second brackets to give 6.
= x + 3x + 2x + 6 Write each term down as you work it out.
2
= x + 5x + 6 Collect together like terms, 3x + 2x = 5x, to simplify your answer.
2
2
b (y + 8)(y − 4) First, multiply the y in the first brackets by the y in the second brackets to give y .
Then, multiply the y in the first brackets by the −4 in the second brackets to give −4y.
Then, multiply the 8 in the first brackets by the y in the second brackets to give 8y.
Finally, multiply the 8 in the first brackets by the −4 in the second brackets to give
−32.
2
= y − 4y + 8y − 32 Write each term down as you work it out.
2
= y + 4y − 32 Collect like terms, −4y + 8y = 4y, to simplify your answer.
) Exercise 9.7

1 Copy and complete these multiplications.

a (x + 4)(x + 1) = x + 1x + x + b (x − 3)(x + 6) = x + 6x − x −
2
2
2
2
= x + x + = x + x −
c (x + 2)(x − 8) = x − x + x − d (x − 4)(x − 1) = x − x − x +
2
2
2
2
= x − x − = x − x +
2 Expand and simplify.
a (x + 3)(x + 7) b (x + 1)(x + 10) c (x + 5)(x − 3)
d (x − 4)(x + 8) e (x − 7)(x − 2) f (x − 12)(x − 2)
3 Expand and simplify.
a (y + 2)(y + 4) b (z + 6)(z + 8) c (m + 4)(m − 3)
d (a − 9)(a + 2) e (p − 6)(p − 5) f (n − 10)(n − 20)
4 Which is the correct expansion of the expression, A, B or C?
a (w + 9)(w + 3) = A w + 6w + 27 B w + 12w + 12 C w + 12w + 27
2
2
2
b (x + 1)(x − 5) = A x − 6x − 5 B x − 4x − 5 C x + 4x − 5
2
2
2
c (y − 8)(y + 6) = A y − 2y − 48 B y − 2y − 14 C y + 2y − 48
2
2
2
d (z − 4)(z − 5) = A z − z + 9 B z − 9z − 20 C z − 9z + 20
2
2
2
5 Copy and complete each expansion.
a (x + 2) = (x + 2)(x + 2) b (x − 3) = (x − 3)(x − 3)
2
2
2
2
= x + 2x + x + = x − 3x − x +
2
2
= x + x + = x − x +
94 9 Expressions and formulae