Let’s solve each problem step by step.
We are given expressions like:
(x + a)(x - a)
This is a special pattern called the
difference of squares.
It always expands to:
x² - a²
Why? Let’s check with the first one:
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1. (x + 1)(x - 1)
Multiply using FOIL (First, Outer, Inner, Last):
= x·x + x·(-1) + 1·x + 1·(-1)
= x² - x + x - 1
= x² - 1
✔
So yes — it becomes
x² minus the square of the number.
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Now apply this to all:
2. (x + 2)(x - 2) = x² - 4
(because 2² = 4)
3. (x + 3)(x - 3) = x² - 9
(3² = 9)
4. (x + 4)(x - 4) = x² - 16
(4² = 16)
5. (x + 5)(x - 5) = x² - 25
(5² = 25)
6. (x + 6)(x - 6) = x² - 36
(6² = 36)
7. (x + 7)(x - 7) = x² - 49
(7² = 49)
8. (x + 8)(x - 8) = x² - 64
(8² = 64)
9. (x + 10)(x - 10) = x² - 100
(10² = 100)
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All done! Just remember: when you have (x + a)(x - a), just write x² - a².
Final Answer:
(x + 1)(x - 1) = x² - 1
(x + 2)(x - 2) = x² - 4
(x + 3)(x - 3) = x² - 9
(x + 4)(x - 4) = x² - 16
(x + 5)(x - 5) = x² - 25
(x + 6)(x - 6) = x² - 36
(x + 7)(x - 7) = x² - 49
(x + 8)(x - 8) = x² - 64
(x + 10)(x - 10) = x² - 100
Parent Tip: Review the logic above to help your child master the concept of 8th grade pre algebra worksheet.
