Question

Factorize (5+3p)^2 -225

Answer 1

Identity to be used: a² - b² = (a + b)(a - b)

(5 + 3p)² - 225

= (5 + 3p)² - (15)²

= [(5 + 3p) + (15)]·[(5 + 3p) - (15)]

= (20 + 3p)(- 10 + 3p)

More identities:-

• (a ± b)² = a² ± 2ab + b²
• (a ± b)³ = a³ ± b³ ± 3ab(a ± b)

{Find a³ + b³ and a³ - b³ using the above identity}

• (a + b + c)² = a² + b² + c² + 2(ab + bc + ca)
• (x + a)(x + b) = x² + (a + b)x + ab
• a³ - b³ = (a - b)(a² + ab + b²)
• a³ + b³ = (a + b)(a² - ab + b²)
• 4ab = (a + b)² - (a - b)²
• 2(a² + b²) = (a + b)² + (a - b)².