please help me to factor binomials

Question

• a²b² - 25c²
• a³ - 8b³
• 27x³ + y³
• 8x³ - 27y³
• (x + y)² - m²
• (x - y)³ + y³

Answer 1

• Formulae used
• a^2-b^2=(a+b)(a-b)
  a^3 - b^3 = (a - b)(a^2 + ab + b^2)
  a^3 + b^3 = (a + b)(a^2 -ab + b^2)
•  
• a²b² - 25c²=(ab)^2-(5c)^2=(ab+5c)(ab-5c)
• a³ - 8b³=a^3-(2b)^3=(a-2b)(a^2+2ab+4b^2)
• 27x³ + y³=(3x)^3+y^3=(3x+y)(9x^2-3xy+y^2)
• 8x³ - 27y³=(2x)^3-(3y)^3=(2x-3y)(4x^2+6xy+9y^2)
• (x + y)² - m²=(x+y+m)(x+y-m)
• (x - y)³ + y³=(x-y+y)[(x-y)^2-(x-y)(y)+y^2]
•                           =(x)(x^2-2xy+y^2-xy+y^2+y^2)
•                           =(x)(x^2-3xy+3y^2)
•