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.

9) i can't see the angle so whatever it is just do this: cos(angle) x hypotenuse and then use that answer and they hypotenuse and plug it into this: (answer you just got)^2 + b^2 = (hypotenuse)^2. the first answer will be the answer of the adjacent side and the second answer after this equation will be the opposite side.

10) y = 14 x = √147 or 12.12435565

11) x = 4.8

12) x = 4.2

13) x = 9.3

14) pq: 13.2

qr : 17.6

angle p: 53º

15) angle c: 54.3º

angle a: 35.7º

16) h = 21040

v = 1841

step-by-step explanation:

10) 7/sin(30) = 14 = y

7^2 + b^2 = 14^2

49 + b^2 = 196

b^2 = 196 - 49

√b^2 = √147

x = √147

11) cos(70) x 14 = 4.788282007

x = 4.8

12) tan(25) x 9 = 4.196768923

x = 4.2

13) sin(31) x 18 = 9.270685348

x = 9.3

14) pq: sin(37) x 22 = 13.23993051

pq: 13.2

qr: cos(37) x 22 = 17.56998122

qr : 17.6

angle p: 180 - (37 + 90) = 53º

15) cos-1(7/12) = 54.31466529

angle c: 54.3º

angle a: 180 - (90 + 54.31466529) = 35.68533471

angle a: 35.7º

16) 4 x 5280 = 21120

cos(5) x 21120

h = 21039.63202

h = 21040

sin(5) x 21120

v = 1840.729287

v = 1841