Page 38 - 新思维数学学生用书9 样章
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2.4 Expanding the product of two linear expressions
Worked example 2.4
Expand and simplify these expressions.
a (x + 2)(x + 3) b (y + 8)(y − 4)
Answer
a (x + 2)(x + 3) First, multiply the x in the first brackets by the x in the second
brackets to give x .
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Then, multiply the x in the first brackets by the 3 in the second
brackets to give 3x.
Then, multiply the 2 in the first brackets by the x in the second
brackets to give 2x.
Finally, multiply the 2 in the first brackets by the 3 in the second
brackets to give 6.
= x + 3x + 2x + 6 Write each term as you work it out.
2
= x + 5x + 6 Collect like terms, 3x + 2x = 5x, to simplify your answer.
2
b (y + 8)( y − 4) First, multiply the y in the first brackets by the y in the second
brackets to give y .
2
Then, multiply the y in the first brackets by the −4 in the second
brackets to give −4y.
Then, multiply the 8 in the first brackets by the y in the second
brackets to give 8y.
Finally, multiply the 8 in the first brackets by the −4 in the second
brackets to give −32.
= y − 4y + 8y – 32 Write each term as you work it out.
2
= y + 4y – 32 Collect like terms, −4y + 8y = 4y, to simplify your answer.
2
