Page 27 - 新思维数学活动用书8 样章

2 Expressions, formulae and equations

11 Copy and complete each factorisation.
a 2a + 4h + 8 = 2(a + 2h + ) b 5b − 25 + 5j = 5(b − + j)

c 12tu + 16u − 20 = 4(3tu + − 5) d 3e + 4e + ef = e(3e + + )
2
e 7k − k − ak = k( − − )
2
f 6n − 9n + 3mn = 3n( − + )
2

Challenge

12 a Copy and complete this spider diagram.
The four expressions around the edge are all equivalent to the expression in the middle.

( + 8x) (12x + )

24x + 32x 2

x( + ) ( + 4x)

b Which expression around the edge is the correct fully factorised expression?

13 a Expand and simplify 4(2x + 3) + 5(x − 4) + 3(5 − 2x)
b Factorise your answer to part a.
14 Read what Zara says.
When I expand

5(3x − 2) − 5(2 + x), then collect
like terms and finally factorise
the result, I get the expression
20(x − 1).

Show that Zara is wrong.
Explain the mistake she has made.

15 Awen expands an expression, collects like terms and
factorises the result.
Work out the missing terms.

2a( + 4) − 4(a + ) + 6a(a − 8) = 8(a − − 2)
2
2
16 The diagram shows a rectangle.
The area of the rectangle is 12b − 30b 6b A
2
Write an expression for
a the length of the rectangle
length
b the perimeter of the rectangle.

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