Question

Factorize: 27 - 125x3 + 225x2 - 135x

Answer 1

Step-by-step explanation:

member the identity

\begin{gathered}( {a - b)}^{3} = ( {a}^{3} - {b}^{3} - 3 {a}^{2} b + 3a {b}^{2} ) \\ try \: to \: apply \: this \: identity \: in \: your \: question \\ {(3)}^{3} - ( {5x)}^{3} - 3( {3)}^{2} (5x) + 3(3)( {5x)}^{2} \\ = 27 - 125 {x}^{3} - 135x + 225 {x}^{2} \\ is \: equal \: to \: given \: polynomial \\ so \:this \: can \: be \: written \: as \\ ( {3 - 5x)}^{3} are \: the \: factors \: of \: given \: polynomial\end{gathered}

(a−b)

3

=(a

3

−b

3

−3a

2

b+3ab

2

)

trytoapplythisidentityinyourquestion

(3)

3

−(5x)

3

−3(3)

2

(5x)+3(3)(5x)

2

=27−125x

3

−135x+225x

2

isequaltogivenpolynomial

sothiscanbewrittenas

(3−5x)

3

arethefactorsofgivenpolynomial