Factor the following polynomials: 1.) 100a² - 25b²
2.) m³ + 125
3.) 8a³ - 64b³
4.) x² - 8x + 12
5.) b² - 6b - 27

Step-by-step explanation:

1. 100a²-25b² [use : a²-b² formula : (a+b)(a-b)]

=> 25(4a²-b²)

=> 25(2a-b)(2a+b).

2. m³+125 [use : a³+b³ formula: (a+b)(a²-ab+b²]

=> m³+5³ => (m+5)(m²-5m+25).

3. 8a³-64b³ [use : a³-b³ formula: (a-b)(a²+ab+b²]

=> 8(a³-8b³) => 8(a-2b)(a²+2ab+b²)

4. x² - 8x + 12 [middle term breaking)

=> x²-2x-6x+12 => x(x-2)-6(x-2) => (x-2) (x-6)

5. b² - 6b - 27 [ middle term breaking]

=> b²-9b+3b-27 => b(b-9)+3(b-9) => (b-9)(b+3).

hope this helps you.

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