Answer:
1. 4(x² + 7x - 9)
2. (5x² - 3y⁵) (25x⁴ + 15x²y⁵ + 9y¹⁰)
3. 20x² - 67x + 56
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