Algebra worksheet for expanding binomial expressions into sums.

To solve these problems, we use a special pattern in algebra called the Difference of Squares.

The rule is:
$$(x + a)(x - a) = x^2 - a^2$$

This means when you multiply two binomials where one is adding a number and the other is subtracting the same number, the middle terms cancel out. You just square the first term ($x$) and subtract the square of the second number ($a$).

Let's go through them one by one:

1. $(x + 1)(x - 1)$
* Square $x$: $x^2$
* Square $1$: $1^2 = 1$
* Result: $x^2 - 1$

2. $(x + 2)(x - 2)$
* Square $x$: $x^2$
* Square $2$: $2^2 = 4$
* Result: $x^2 - 4$

3. $(x + 3)(x - 3)$
* Square $x$: $x^2$
* Square $3$: $3^2 = 9$
* Result: $x^2 - 9$

4. $(x + 4)(x - 4)$
* Square $x$: $x^2$
* Square $4$: $4^2 = 16$
* Result: $x^2 - 16$

5. $(x + 5)(x - 5)$
* Square $x$: $x^2$
* Square $5$: $5^2 = 25$
* Result: $x^2 - 25$

6. $(x + 6)(x - 6)$
* Square $x$: $x^2$
* Square $6$: $6^2 = 36$
* Result: $x^2 - 36$

7. $(x + 7)(x - 7)$
* Square $x$: $x^2$
* Square $7$: $7^2 = 49$
* Result: $x^2 - 49$

8. $(x + 8)(x - 8)$
* Square $x$: $x^2$
* Square $8$: $8^2 = 64$
* Result: $x^2 - 64$

9. $(x + 10)(x - 10)$
* Square $x$: $x^2$
* Square $10$: $10^2 = 100$
* Result: $x^2 - 100$

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