Question

factorise
8a^3 - b^3​

Answer 1

Required Answer:-

Given to Factorise:

• 8a³ - b³

Answer:

• The factorised form is (2a - b)(4a² + 2ab + b²)

Solution:

$\sf 8 {a}^{3} - {b}^{3}$

$\sf = {(2a)}^{3} - {(b)}^{3}$

It's in the form of x³ - y³. Factorise it.

$\sf = (2a - b)(4{a}^{2} + 2ab + {b}^{2} )$

Hence, the factorised form is (2a - b)(4a² + 2ab + b²)

Identity Used:

• $\sf {x}^{3} - {y}^{3} = (x - y)( {x}^{2} + xy + {y}^{2} )$

Other Identities:

• $\sf {x}^{2} + 2xy + {y}^{2} = {(x + y)}^{2}$
• $\sf {x}^{2} - 2xy + {y}^{2} = {(x - y)}^{2}$
• $\sf {x}^{2} - {y}^{2} = (x + y)(x - y)$
• $\sf {x}^{3} + {y}^{3} = (x + y)( {x}^{2} - xy + {y}^{2} )$

Answer 2

Answer:

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