Question

factorise. a3x2+2abx3+b3x​

Answer 1

\begin{gathered} {a}^{3} {x}^{3} - 3 {a}^{2} b {x}^{2} + 3a {b}^{2} x - {b}^{3 } \\ compare \: this \: expression \: with \: the \: identity \\ ( {x - y)}^{3} = {x}^{3} - 3 {x}^{2} y + 3x {y}^{2} - {y}^{3} \\ so \\ ( {ax)}^{3} - 3( {ax)}^{2} y + 3ax {y}^{2} - ( {y)}^{3} \\ = ( {ax - b)}^{3} \\ so \: factors \: are \: (ax - b)(ax - b)(ax - b)\end{gathered}

a

3

x

3

−3a

2

bx

2

+3ab

2

x−b

3

comparethisexpressionwiththeidentity

(x−y)

3

=x

3

−3x

2

y+3xy

2

−y

3

so

(ax)

3

−3(ax)

2

y+3axy

2

−(y)

3

=(ax−b)

3

sofactorsare(ax−b)(ax−b)(ax−b)

Answer 2

thanks for your free points