Page 40 - 新思维数学学生用书9 样章

2.4 Expanding the product of two linear expressions

Think like a mathematician

5 Work with a partner to answer this question.
a Look at this expansion. (x + 5)(x + 4) = x + 5x + 4x + 20 = x + 9x + 20
2
2
How would the expansion change if the red + sign changed to − ?
b Here is the expansion again. (x + 5)(x + 4) = x + 5x + 4x + 20 = x + 9x + 20
2
2
How would the expansion change if the red + sign changed to − ?
c Here is the expansion again. (x + 5)(x + 4) = x + 5x + 4x + 20 = x + 9x + 20
2
2
How would the expansion change if both of the + signs changed to − signs?
d Write down the missing signs (+ or −) in these expansions.
In each expression, the number represented by A is greater than the
number represented by B. C is the sum of A and B in each equation, and D

is the product of A and B in each equation.
i (x + A)(x + B) = x Cx D
2
ii (x + A)(x − B) = x Cx D
2
iii (x − A)(x + B) = x Cx D
2
iv (x − A)(x − B) = x Cx D
2
Discuss your answers to these questions with other learners in your class.

6 Which is the correct expansion of the expression, A, B or C?

Use what you have learned from Question 5 to help you.
a (w + 9)(w + 3) = A w + 12w − 27 B w − 12w + 27 C w + 12w + 27
2
2
2
b (x + 7)(x − 5) = A x + 2x − 35 B x − 2x + 35 C x − 2x − 35
2
2
2
c (y − 8)(y + 6) = A y − 2y + 48 B y − 2y − 48 C y + 2y − 48
2
2
2
d (z − 4)(z − 5) = A z − 9z + 20 B z − 9z − 20 C z + 9z + 20
2
2
2
7 Copy and complete each expansion.
2
a (x + 2) = (x + 2)(x + 2) b (x − 3) = (x − 3)(x − 3)
2
2
= x + 2x + x + = x − 3x − x +
2
2
= x + x + = x − x +
2
8 a Expand and simplify each expression. Tip
i (y + 5) 2 ii (z + 1) 2 iii (m + 8) 2
iv (a − 2) 2 v (p − 4) 2 vi (n − 9) 2 Use the same method
b Look carefully at your answers to part a. as in Question 7.
Use these answers to complete the general
expansion: (x + a) = x + x + Tip
2
2
This type of expansion is
called a perfect square.

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