Factorise completely 4mn−16n2−4m2n+64n34mn - 16n^2 - 4m^2n + 64n^3. Answer ...

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Worked solution

12

1. Take out the highest common factor from all terms.

4mn−16n2−4m2n+64n3=4n(m−4n−m2+16n2)4mn-16n^2-4m^2n+64n^3=4n(m-4n-m^2+16n^2)

2. Rearrange the terms inside the bracket to expose a difference of squares.

4n(m−4n−m2+16n2)=4n{−(m2−16n2)+(m−4n)}4n(m-4n-m^2+16n^2)=4n\{-(m^2-16n^2)+(m-4n)\}

3. Factorise completely by grouping with the common factor $(m-4n)$.

4n{−(m2−16n2)+(m−4n)}=4n{−(m−4n)(m+4n)+(m−4n)}=4n(m−4n)(1−m−4n)=−4n(m−4n)(m+4n−1)\begin{aligned} 4n\{-(m^2-16n^2)+(m-4n)\} &=4n\{-(m-4n)(m+4n)+(m-4n)\}\\ &=4n(m-4n)(1-m-4n)\\ &=-4n(m-4n)(m+4n-1) \end{aligned}
Answer

−4n(m−4n)(m+4n−1)-4n(m-4n)(m+4n-1)

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