Question

50 POINTS please show the step by step process.I already know the answers i just the steps!!

1.Factor: 4x^2+28x-36

2.Factor: 125x^6-27y^15

3.Multiply: (4x-7)(5x-8)

Answer 1

Answer:

1.   4(x² + 7x - 9)

2.  (5x² - 3y⁵) (25x⁴ + 15x²y⁵ + 9y¹⁰)

3.  20x² - 67x + 56

Step-by-step explanation:

1.  factor 4x^2+28x-36

= 4x² + 28x - 36

re-write 36=4*9,  and 28=4*7

= 4x² + 4 * 7x - 4 * 9

factor out common term:

= 4(x² + 7x - 9)

2.  factor 125x^6-27y^15

= 125x⁶ - 27y¹⁵

=(5x²)³ - (3y⁵)₃

apply difference of cubes: x³-y³ = (x-y)(x²+xy+y²)

= (5x² - 36y⁵)(5²x⁴ + 5 * 3x²y⁵ + 3²y¹⁰)

refine:

= (5x² - 3y⁵) (25x⁴ + 15x²y⁵ + 9y¹⁰)

3. multiply (4x-7)(5x-8)

apply the FOIL method

= 4x * 5x + 4x (-8) + (-7) * 5x + (-7) (-8)

= 20x² - 67x + 56