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? Because when you multiply:
(x + a)(x - a) = x·x + x·(-a) + a·x + a·(-a)
= x² - ax + ax - a²
The middle terms (-ax and +ax) cancel out, leaving just x² - a².
So we can use this shortcut for every problem!
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1. (x + 1)(x - 1) → x² - 1² =
x² - 1
2. (x + 2)(x - 2) → x² - 2² =
x² - 4
3. (x + 3)(x - 3) → x² - 3² =
x² - 9
4. (x + 4)(x - 4) → x² - 4² =
x² - 16
5. (x + 5)(x - 5) → x² - 5² =
x² - 25
6. (x + 6)(x - 6) → x² - 6² =
x² - 36
7. (x + 7)(x - 7) → x² - 7² =
x² - 49
8. (x + 8)(x - 8) → x² - 8² =
x² - 64
9. (x + 10)(x - 10) → x² - 10² =
x² - 100
(Note: The original list skips (x+9)(x-9), but that’s okay — we’ll do what’s asked.)
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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 algebra worksheet 8th grade.
