Page 41 - 新思维数学学生用书9 样章

2 Expressions and formulae

9 a Show that when you expand and simplify (x + 3)(x − 3) you Tip

will have an expression with only two terms.
b Expand and simplify these expressions. This type of
i (x + 2)(x − 2) ii (x − 5)(x + 5) iii (x + 7)(x − 7) expansion
c What do you notice about your answers in part b? is called the
d Use your answer to part c to write the simplified expansion of difference of

(x − 10)(x + 10). two squares.
e Look carefully at your answers to this question so far.
Use these answers to complete the general expansion: (x + a)(x – a) = x –
2

Activity 2.4

Work with a partner on this activity.
Here is part of a number grid. 1 2 3 4 5
Look at the red block of four squares, and follow 6 7 8 9 10

these steps. 11 12 13 14 15
1 Multiply the number in the bottom 16 17 18 19 20
left square by the number in the top right 21 22 23 24 25

square: 9 × 5 = 45 26 27 28 29 30
2 Multiply the number in the top left square 31 32 33 34 35
by the number in the bottom right 36 37 38 39 40
square: 4 × 10 = 40
3 Subtract the second answer from the first: 45 − 40 = 5

a Repeat these three steps with the blue block of four squares.
b Repeat these three steps with the green block of four squares.
c What do you notice about your answers to parts a and b?

d Here is a general block of four squares from the same number grid. n
Copy the block of four squares and write an expression, in terms
of n, in each of the other squares to represent the missing numbers.
e Repeat the three steps with the block of four squares in part d.
What do you notice about your answer?

Now you have completed this activity, compare your answers with other
learners in your class. Discuss any differences in your answers and explain any
mistakes that have been made.

Summary checklist

I can expand two brackets.

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