Question

factor of polynomial is 216a³-125​

Answer 1

Answer:

Step-by-step explanation:

216a³-125

=(6a)³-5³

=(6a-5){(6a)²+5²+6a×5}

=(6a-5)(36a²+25+30a).

Answer 2

$\large\bf\underline \blue {To \: \mathscr{f}ind:-}$

• we need to factorize 216a³ - 125

$\huge\bf\underline \purple{ \mathcal{S}olution:-}$

↛ 216a³ - 125

• we know that
• 216 is the cube of 6
• 125 is the cube of 5

↛ (6a)³ - 5³

• By using identity
• a³ - b³ = (a - b)(a² + b² + ab)

↛ (6a)³ - 5³ = (6a - 5)[(6a)² + (5)² + 6a × 5]

↛ (6a - 5) [36² + 25 + 30a]

Hence,

• 216a³ - 125 = (6a - 5) [36² + 25 + 30a]

━━━━━━━━━━━━━━━━━━━━━━━━━

⠀⠀⠀⠀⠀✫★Some identities:-

» (a + b)² = a² + b² + 2ab

» (a - b)² = a² + b² - 2ab

» (a + b)(a - b) = a² - b²

» (a + b + c)² = a² + b² + c² + 2ab + 2bc + 2ac

» a³ + b³ = (a + b)(a² + b² - ab)

» a³ - b³ = (a - b)(a² + b² + ab)

━━━━━━━━━━━━━━━━━━━━━━━━━