It looks like you've uploaded an image with a math task that asks you to
distribute and expand each expression into a sum. The expressions are all in the form of:
$$
(x + a)(x - a)
$$
This is a
difference of squares pattern, which follows the identity:
$$
(x + a)(x - a) = x^2 - a^2
$$
Let’s go through each one step by step.
---
1. $(x + 1)(x - 1)$
Using the difference of squares:
$$
= x^2 - (1)^2 = x^2 - 1
$$
---
2. $(x + 2)(x - 2)$
$$
= x^2 - (2)^2 = x^2 - 4
$$
---
3. $(x + 3)(x - 3)$
$$
= x^2 - (3)^2 = x^2 - 9
$$
---
4. $(x + 4)(x - 4)$
$$
= x^2 - (4)^2 = x^2 - 16
$$
---
5. $(x + 5)(x - 5)$
$$
= x^2 - (5)^2 = x^2 - 25
$$
---
6. $(x + 6)(x - 6)$
$$
= x^2 - (6)^2 = x^2 - 36
$$
---
7. $(x + 7)(x - 7)$
$$
= x^2 - (7)^2 = x^2 - 49
$$
---
8. $(x + 8)(x - 8)$
$$
= x^2 - (8)^2 = x^2 - 64
$$
---
9. $(x + 10)(x - 10)$
$$
= x^2 - (10)^2 = x^2 - 100
$$
---
✔ Final Answers:
1. $x^2 - 1$
2. $x^2 - 4$
3. $x^2 - 9$
4. $x^2 - 16$
5. $x^2 - 25$
6. $x^2 - 36$
7. $x^2 - 49$
8. $x^2 - 64$
9. $x^2 - 100$
---
🔍 Explanation:
Each expression is of the form $(x + a)(x - a)$, which simplifies using the
difference of squares formula:
$$
(a + b)(a - b) = a^2 - b^2
$$
Here, $a = x$, and $b = n$ (the number), so:
$$
(x + n)(x - n) = x^2 - n^2
$$
This shortcut avoids having to use the distributive property (FOIL) every time and gives the result directly.
Let me know if you'd like to see the FOIL method applied to any of them!
Parent Tip: Review the logic above to help your child master the concept of 8th grade algebra worksheet.
