Question

Resolve into factors

a³-125

Please give step by step explanation​

Answer 1

Answer:

(a-5) (a²+5a+5²)

Step-by-step explanation:

$a {}^{3} - 125 \\ 125 = 5 {}^{3} \\ we \: know \: that \: \\ x {}^{3} - y {}^{3} = (x - y)(x {}^{2} + xy + y {}^{2} ) \\ proof \: that \: why \: x {}^{3} - y {}^{} \\ = (x - y)(x {}^{2} + xy + y {}^{2} ) \\ let \: us \: start \\ (x - y)(x {}^{2} + xy + y {}^{2} ) \\ x {}^{3} + x {}^{2} y + xy {}^{2} - x {}^{2} y - xy {}^{2} - y {}^{3} \\ x {}^{3} + (x {}^{2} y - x {}^{2} y)(xy {}^{2} - xy {}^{2} ) - y {}^{3} \\ x {}^{3} + 0 + 0 - y {}^{3} \\ x {}^{3} - y {}^{3} \\ therefore \\ a {}^{3} - 5 {}^{3} \\ = > (a - 5)(a {}^{2} + 5a + 5 {}^{2} )$

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