Chapter 4 Algebra Worksheet Page 38
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502 1 3
4 F W O R K I N G W I T H B R A C K E T S
12
Demonstrate that each statement is true by fi nding the appropriate areas in the
diagram.
2
a
3(a + 2) = 3a + 6
b
x(x + 4) = x
+ 4x
x + 4
a + 2
x
x
3
3
a
2
x
4
13
Draw a diagram to demonstrate that each statement is true.
2
a
6(k + 8) = 6k + 48
b
4(2d + 9) = 8d + 36
c
2p(p + 3) = 2p
+ 6p
14
This diagram can be used to demonstrate that
a
5(a − 3) = 5a − 15.
rectangle
rectangle
What is the length and width of rectangle 1?
a
5
5
1
2
Use your answer to part
to write an expression
b
a
for the area of rectangle 1 using brackets.
a − 3
3
Another way to work out the area of rectangle 1 is to
c
subtract the area of rectangle 2 from the total area of the large rectangle.
i
Write the length and width of the large rectangle.
ii
Use these length and width measurements to write an expression for the area
of the large rectangle.
Write the length and width of rectangle 2.
iii
Use these length and width measurements to write an expression for the area
iv
of rectangle 2.
Use your answers to parts
and
to write an expression for the area of
v
ii
iv
rectangle 1.
d
Explain how you were able to show that 5(a − 3) = 5a − 15.
15
Draw a diagram and fi nd appropriate areas of rectangles to demonstrate why each
statement is true.
2
a
4(x − 2) = 4x − 8
b
c(d − 5) = cd − 5c
c
h(h − 4) = h
− 4h
16
Expand and simplify each expression.
2
3
4
a
3x
(4x
− 7) − 5x
(x + 2)
3
2
2
a
(ab + c − 1) + a
(3ac − a
b + a)
b
2
2
2
2
2
2m(3m
+ 5mn) − 6n(m
+ m
− 4)
c
np
p
2
3
2
d
5w(4w
x − 3y) + 2y(9w − 6xy) − 4x(5w
− 3y
)
17
Evaluate each expression in question
16
using these values:
a = −3, b = 7, c = 4
Reflect
m = 2, n = −4, p = −1
w = −5, x = 2, y = −6.
What is the distributive law and
how is it used?
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