Question

Factorise




8a^3 b - 10 a^2 b^2 - 12 a b^3​

Answer 1

Answer:

QUESTION

➡

\begin{gathered}\bold{Factorise \: \: the \: \: following \: : }\\ \\ \boxed{8 a {}^{3} - b {}^{3} - 12a{}^{2}b + 6ab {}^{2} }\end{gathered}

Factorisethefollowing:

8a

3

−b

3

−12a

2

b+6ab

2

\underline{\underline{SOLUTION}}

SOLUTION

➡

\begin{gathered}\bold{We \: \: know \: \: that} \\ \\ \boxed{(x - y) {}^{3} = x {}^{3} - y {}^{3} - 3x {}^{2}y + 3xy {}^{2} } \\ \\ \\ \underline{\bold{ \: \: By \: \: using \: \: this \: \: formula \: \: }}\end{gathered}

Weknowthat

(x−y)

3

=x

3

−y

3

−3x

2

y+3xy

2

Byusingthisformula

\begin{gathered}8a {}^{3} - b {}^{3} - 12 a {}^{2} b + 6ab {}^{2} \\ \\ = (2a) {}^{3} - b {}^{3} - 3 \times( 2a) {}^{2} \times b + 3 \times 2a \times b {}^{2} \\ \\ = ( 2a - b) {}^{3} \\ \\ = (2a - b)(2a - b)(2a - b)\end{gathered}

8a

3

−b

3

−12a

2

b+6ab

2

=(2a)

3

−b

3

−3×(2a)

2

×b+3×2a×b

2

=(2a−b)

3

=(2a−b)(2a−b)(2a−b)