https://file.aiquickdraw.com/mathbot/file/1725972204784v69nzizh.jpg

Let's go through the factoring exercises in the image you provided. Here is a breakdown of each section:

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### A: Factoring by common monomial factor
In this section, we factor out the greatest common factor (GCF) from each expression.

1. **a.** \( 30qpr - 5qp + 5qf + 28m^4 + 40m^3 + 8 \)
2. **b.** \( 45x^2 - 25g + 30b^2 + 5ab - 15a^2 \)
3. **c.** \( 56 - 35ph, 50x - 80y \)
4. **d.** \( 7ab - 35a^2, 27x^2y^5 - 72xy^2 \)
5. **e.** \( 20x^4 - 30x + 30j, 8x^3y + 4xy \)

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### B: Factoring by difference of two squares
These involve factoring expressions of the form \( a^2 - b^2 \), which factor into \( (a - b)(a + b) \).

1. **a.** \( a^2 - 49f, 4x^2 - 25 \)
2. **b.** \( p^2 - 144g, 9a^2 - 4 \)
3. **c.** \( x^2 - 9, 9b^2 - 121 \)
4. **d.** \( k^2 - 121, 16r^2 - 25 \)
5. **e.** \( n^2 - 289, 25m^2 - 9 \)

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### C: Factoring sum and difference of cubes
In this section, we use formulas for factoring sums and differences of cubes:

- \( a^3 + b^3 = (a + b)(a^2 - ab + b^2) \)
- \( a^3 - b^3 = (a - b)(a^2 + ab + b^2) \)

1. **a.** \( x^3 + 8, a^3 - 216 \)
2. **b.** \( a^3 + 216, 27m^3 - 125 \)
3. **c.** \( 432 + 250m, 64x^3 - 27 \)
4. **d.** \( a^3 + 64i, x^3 - 64 \)
5. **e.** \( 27 + 8x^3, 64x^3 - 27y^3 \)

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Would you like to go through a specific part in more detail or get solutions for a particular set? Here are 5 relative questions:

1. Would you like to factor one of these problems step by step?
2. Do you need help identifying the greatest common factor in section A?
3. Can I help you with a review of the difference of squares formula?
4. Would you like examples of other polynomials factored by cubes?
5. Do you need assistance with any specific polynomial identities?

**Tip**: Always start by identifying the common factor before diving into more complex factoring techniques.

Factoring polynomials using common monomial factors, difference of two squares, and sum or difference of cubes.

Learn how to factor polynomials by identifying common monomial factors, factoring the difference of two squares, and using formulas for the sum and difference of cubes. This guide provides step-by-step solutions to common algebraic expressions for high school students.

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