EXERCISE 5 (a) Expand and simplify: $$ \begin{array}{lllll} ext { (1) }(x+7)(x-7) & ext { (2) } & (x-3)(x+3) & ext { (3) } & (2 x-1)(2 x+1) \ ext { (4) } & (9 x+4)(9 x-4) & ext { (5) } & (3 x-2 y)(3 x+2 y) & ext { (6) } \ \left(4 a^{3} b+3 ight)\left(4 a^{3} b-3 ight) \ ext { (7) } & \left(6-3 x^{4} y ight)\left(6+3 x^{4} y ight) & ext { (8) } & (3 x-2+y)(3 x-2-y)\end{array} $$ $$ \begin{array}{lll} ext { (9) } & \left(1-a^{4} ight)\left(1-a^{2} ight)\left(1+a^{2} ight) & \end{array} $$

Question

EXERCISE 5 (a) Expand and simplify: $$ \begin{array}{lllll}	ext { (1) }(x+7)(x-7) & 	ext { (2) } & (x-3)(x+3) & 	ext { (3) } & (2 x-1)(2 x+1) \ 	ext { (4) } & (9 x+4)(9 x-4) & 	ext { (5) } & (3 x-2 y)(3 x+2 y) & 	ext { (6) } \ \left(4 a^{3} b+3ight)\left(4 a^{3} b-3ight) \ 	ext { (7) } & \left(6-3 x^{4} yight)\left(6+3 x^{4} yight) & 	ext { (8) } & (3 x-2+y)(3 x-2-y)\end{array} $$ $$ \begin{array}{lll}	ext { (9) } & \left(1-a^{4}ight)\left(1-a^{2}ight)\left(1+a^{2}ight) & \end{array} $$

UpStudy AI · Accepted Answer

Certainly! Let's expand and simplify each of the given expressions step by step.

### (a) Expand and Simplify:

1. **$$(x + 7)(x - 7)$$**
   $$
   = x^2 - 7x + 7x - 49 \
   = x^2 - 49
   $$
   **Simplified Form:** $$x^2 - 49$$

2. **$$(x - 3)(x + 3)$$**
   $$
   = x^2 + 3x - 3x - 9 \
   = x^2 - 9
   $$
   **Simplified Form:** $$x^2 - 9$$

3. **$$(2x - 1)(2x + 1)$$**
   $$
   = (2x)^2 - (1)^2 \
   = 4x^2 - 1
   $$
   **Simplified Form:** $$4x^2 - 1$$

4. **$$(9x + 4)(9x - 4)$$**
   $$
   = (9x)^2 - (4)^2 \
   = 81x^2 - 16
   $$
   **Simplified Form:** $$81x^2 - 16$$

5. **$$(3x - 2y)(3x + 2y)$$**
   $$
   = (3x)^2 - (2y)^2 \
   = 9x^2 - 4y^2
   $$
   **Simplified Form:** $$9x^2 - 4y^2$$

6. **$$(4a^{3}b + 3)(4a^{3}b - 3)$$**
   $$
   = (4a^{3}b)^2 - (3)^2 \
   = 16a^{6}b^2 - 9
   $$
   **Simplified Form:** $$16a^{6}b^2 - 9$$

7. **$$(6 - 3x^{4}y)(6 + 3x^{4}y)$$**
   $$
   = 6^2 - (3x^{4}y)^2 \
   = 36 - 9x^8y^2
   $$
   **Simplified Form:** $$36 - 9x^8y^2$$

8. **$$(3x - 2 + y)(3x - 2 - y)$$**
   $$
   = (3x - 2)^2 - y^2 \
   = 9x^2 - 12x + 4 - y^2
   $$
   **Simplified Form:** $$9x^2 - 12x + 4 - y^2$$

9. **$$(1 - a^{4})(1 - a^{2})(1 + a^{2})$$**
   $$
   = (1 - a^{4})(1 - a^{2} + a^{2} - a^{4}) \
   = 1 - 2a^4 + a^8
   $$
   **Simplified Form:** $$1 - 2a^4 + a^8$$

---

**Summary of Simplified Expressions:**

1. $$x^2 - 49$$
2. $$x^2 - 9$$
3. $$4x^2 - 1$$
4. $$81x^2 - 16$$
5. $$9x^2 - 4y^2$$
6. $$16a^{6}b^2 - 9$$
7. $$36 - 9x^8y^2$$
8. $$9x^2 - 12x + 4 - y^2$$
9. $$1 - 2a^4 + a^8$$

Feel free to ask if you need further explanations on any of these expansions!
Here are the simplified forms of the given expressions: 1. $$x^2 - 49$$ 2. $$x^2 - 9$$ 3. $$4x^2 - 1$$ 4. $$81x^2 - 16$$ 5. $$9x^2 - 4y^2$$ 6. $$16a^{6}b^2 - 9$$ 7. $$36 - 9x^8y^2$$ 8. $$9x^2 - 12x + 4 - y^2$$ 9. $$1 - 2a^4 + a^8$$

Real Tutor Solution

Answer

Solution

Bonus Knowledge

Related Questions

Latest Algebra Questions