Page 32 - 新思维数学学生用书9 样章

2.3 Expressions and indices

9 a Write an expression for the perimeter of this rectangle. 5 – x 2

b Show that the expression can be simplified to 2(2x + 9). 3x + 4
2
2
c Read what Arun says.
Tip

You might
When x = 2 and
when x = −2, you get need to remind
the same perimeter. yourself how
to factorise
expressions.
Is Arun correct? Explain your answer. Show your working.

10 a A square has an area of 25 cm . Show that the perimeter of the square is 20 cm.
2
b A square has an area of 49 cm . Work out the perimeter of the square.
2
c A square has an area of x cm . Write an expression for the
2
perimeter of the square.
Use your working for parts a and b to help you.
11 a A cube has side length x cm. Write an expression for the volume of the cube.
b A cube has a volume of y cm . Write an expression for the side length of the cube.
3

Summary checklist

I can use letters to represent numbers.
I can use the correct order of operations in algebraic expressions.

2.3 Expressions and indices

In this section you will …

• use the laws of indices in algebraic expressions.

You already know how to use the laws of indices for multiplication and division of numbers. You can
also use these rules with algebraic expressions.
• When you multiply powers of the same variable, you add the indices. x × x = x a+b
b
a
• When you divide powers of the same variable, you subtract the indices. x ÷ x = x a−b
b
a
• When you simplify the power of a power, you multiply the indices. (x ab x ab
×
) =

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