Factorisation Question

Hi,

All of the attached questions involve some factorising, but I seem to be having trouble with them.

For the attachment titled ‘a’ I got: { 2(3k-λ)(3k+λ) + 9λ(k-3[(3k+2λ)^3]) } / (3k+2λ)^2 but don’t know whether that’s right or where to proceed.

For ‘b’ I completed the square and got: (sinx+2)^2-4 but am not sure how to calculate the smallest value.

For ‘c’ I ended up with: 2(n-(1/n))^2+n-1=0 and don’t know how to calculate for n.

Thank you

Original post by samjohnny

Hi,

All of the attached questions involve some factorising, but I seem to be having trouble with them.

For the attachment titled ‘a’ I got: { 2(3k-λ)(3k+λ) + 9λ(k-3[(3k+2λ)^3]) } / (3k+2λ)^2 but don’t know whether that’s right or where to proceed.

For ‘b’ I completed the square and got: (sinx+2)^2-4 but am not sure how to calculate the smallest value.

For ‘c’ I ended up with: 2(n-(1/n))^2+n-1=0 and don’t know how to calculate for n.

Thank you

For the first one, factoruise top and bottom of large fraction and you should be able to cancel a factor. Then combine the fractions over a common denominator and see where you go from there.
For the second one. complete the square of the sin terms and think when it willbe as small as possible. But remember that