https://file.aiquickdraw.com/mathbot/file/1730630773177q4vdhkd1.jpg

Let’s factorise each expression by taking out the common factors.

### Solutions

#### a) \( 2x^2 - 32 \)
* **Factor out 2:**  
  \( 2(x^2 - 16) \)
* **Further factorize \( x^2 - 16 \) as a difference of squares:**  
  \( 2(x + 4)(x - 4) \)

#### b) \( 3x^2 - 108 \)
* **Factor out 3:**  
  \( 3(x^2 - 36) \)
* **Further factorize \( x^2 - 36 \):**  
  \( 3(x + 6)(x - 6) \)

#### c) \( 4a^2 - 100 \)
* **Factor out 4:**  
  \( 4(a^2 - 25) \)
* **Further factorize \( a^2 - 25 \):**  
  \( 4(a + 5)(a - 5) \)

#### d) \( 5y^2 - 20 \)
* **Factor out 5:**  
  \( 5(y^2 - 4) \)
* **Further factorize \( y^2 - 4 \):**  
  \( 5(y + 2)(y - 2) \)

#### e) \( 24a^2 - 6b^2 \)
* **Factor out 6:**  
  \( 6(4a^2 - b^2) \)
* **Further factorize \( 4a^2 - b^2 \):**  
  \( 6(2a + b)(2a - b) \)

#### f) \( 3x^2 - 27y^2 \)
* **Factor out 3:**  
  \( 3(x^2 - 9y^2) \)
* **Further factorize \( x^2 - 9y^2 \):**  
  \( 3(x + 3y)(x - 3y) \)

#### g) \( 8y^2 - 128 \)
* **Factor out 8:**  
  \( 8(y^2 - 16) \)
* **Further factorize \( y^2 - 16 \):**  
  \( 8(y + 4)(y - 4) \)

#### h) \( 80p^2 - 5q^2 \)
* **Factor out 5:**  
  \( 5(16p^2 - q^2) \)
* **Further factorize \( 16p^2 - q^2 \):**  
  \( 5(4p + q)(4p - q) \)

#### i) \( 4x^2 - 64 \)
* **Factor out 4:**  
  \( 4(x^2 - 16) \)
* **Further factorize \( x^2 - 16 \):**  
  \( 4(x + 4)(x - 4) \)

#### j) \( 3x^2 - 3 \)
* **Factor out 3:**  
  \( 3(x^2 - 1) \)
* **Further factorize \( x^2 - 1 \):**  
  \( 3(x + 1)(x - 1) \)

#### k) \( 72p^2 - 2 \)
* **Factor out 2:**  
  \( 2(36p^2 - 1) \)
* **Further factorize \( 36p^2 - 1 \):**  
  \( 2(6p + 1)(6p - 1) \)

#### l) \( 2 - 18x^2 \)
* **Factor out 2:**  
  \( 2(1 - 9x^2) \)
* **Further factorize \( 1 - 9x^2 \):**  
  \( 2(1 + 3x)(1 - 3x) \)

#### m) \( 8a^2 - 18m^2 \)
* **Factor out 2:**  
  \( 2(4a^2 - 9m^2) \)
* **Further factorize \( 4a^2 - 9m^2 \):**  
  \( 2(2a + 3m)(2a - 3m) \)

#### n) \( 125 - 20a^2 \)
* **Factor out 5:**  
  \( 5(25 - 4a^2) \)
* **Further factorize \( 25 - 4a^2 \):**  
  \( 5(5 + 2a)(5 - 2a) \)

#### o) \( 200x^2 - 18y^2 \)
* **Factor out 2:**  
  \( 2(100x^2 - 9y^2) \)
* **Further factorize \( 100x^2 - 9y^2 \):**  
  \( 2(10x + 3y)(10x - 3y) \)

#### p) \( 98m^2 - 8n^2 \)
* **Factor out 2:**  
  \( 2(49m^2 - 4n^2) \)
* **Further factorize \( 49m^2 - 4n^2 \):**  
  \( 2(7m + 2n)(7m - 2n) \)

Would you like further clarification on any of these steps? 

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### Related Questions:
1. How do you determine if a quadratic expression can be factored further?
2. What is the difference between factoring out a common factor and factoring a difference of squares?
3. How do you identify the greatest common factor in polynomials with multiple terms?
4. What is the procedure for factoring a trinomial versus a binomial?
5. How can factorization be applied in solving algebraic equations?

### Tip:
Always check if the terms share a greatest common factor before attempting to use other factoring methods. This step can simplify the process significantly.

Factorise by first taking out a common factor.

Learn to factorize algebraic expressions by first taking out the common factor. This lesson covers factorization techniques, including identifying and using the difference of squares formula. Ideal for students in Grades 8-10.

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