Year 11 Maths - Methods Polynomials

Factorisation Of Polynomials

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Questions

Question 1

28648

Factorise \(8{m^3} - 27{n^3}\)

Answer

\(\left( {2m - 3n} \right)\left( {4{m^2} + 6mn + 9{n^2}} \right)\)

Worked Solution

\begin{align}
&x^{3}-y^{3}=(x-y)\left(x^{2}+x y+y^{2}\right) \\
&\begin{aligned}
8m^{3}-27n^{3}&=(2 m)^{3}-(3 n)^{3} \\
&=(2m-3n)\left(4m^{2}+6mn+9n^{2}\right)
\end{aligned}
\end{align}

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