Page 45 - 新思维数学学生用书7 样章

2 Expressions, formulae and equations

8 Write each expression in its simplest form. Tip

The first one has been done for you.
a 2ab + 3ab + 5pq + 7qp = 5ab + 12pq In part a, start by rewriting
b 3st + 5st + 9pu + 7up 7qp as 7pq.
c 4vb + 2bv + 6ad − 4da In part d, start by rewriting
d 11rt + 9gh − 2rt − 7hg the expression with like terms

e 8xy + 12xz + 3yx − 9zx together and all of the letters in
f 6a + 7ac − 2a + ca alphabetical order, like this:
g 4mn − 3nm + 7gh − 7hg 11rt − 2rt + 9gh − 7gh.

9 This is part of Dai’s homework.

Question
Write these expressions in their simplest form.

a 2x + 8 + 6x − 4 b 3bc + 5bd − 2bc + 3db

Solution
a 2x + 8 + 6x − 4 = 8x + 4 = 12x
b 3bc + 5bd − 2bc + 3db = 5bc + 5bd + 3db

Dai has made several mistakes. Explain what Dai has done wrong.
Work out the correct answers.
10 Copy and complete this algebraic pyramid.

Remember that you find the expression in each block by
4kj +3mp jk +2pm 2kj–mp
adding the expressions in the two blocks below it.

Activity 2.2

Design an algebraic pyramid like the one in Question 10, for a partner to complete.
On a piece of paper, draw your pyramid and fill in the bottom row of the pyramid.
You may use single or double letter terms. You may use addition and subtraction
signs.

Before you ask your partner to complete your pyramid, make sure you write down
the answers on a different piece of paper.
Swap pyramids with a partner, complete their pyramid, then swap back and mark
each other’s work. Discuss any mistakes that have been made.

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