2x + y = 12. P = xy^2. Show that P = 4x^3 - 48x^2 + 144x
We want to make P = xy^2 into something more complicated, which only has Xs, and no Ys.
Firstly, you need to remember that when there are two equations, the question will almost definitely involve substituting one into the other. In this question, it happens to be that that's all there is to it.
By making y the subject of one equation, we can eliminate it from another. In this case we want P = [complicated thing with no x], so we make y the subject of the other equation, to eliminate it from this one.
Making y the subject: 2x + y = 12 ----> y = 12-2x
Substitute that into P = xy^2: P = x(12-2x)^2
Expand = x(144 + 4x^2 - 48x)
= 4x^3 - 48x^2 + 144x
JR
Related Maths A Level answers
All answers ▸Show that sin2A is equal to 2sinAcosA
Differentiate the function X^4 - (20/3)X^3 + 2X^2 + 7. Find the stationary points and classify.
Express the fraction (p+q)/(p-q) in the form m+n√2, where p=3-2√2 and q=2-√2.
The height x metres, of a column of water in a fountain display satisfies the differential equation dx/dt = 8sin(2t)/(3sqrt(x)), where t is the time in seconds after the display begins. (a) Solve the differential equation, given that x(0)=0