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The first step is to differentiate the equation of the curve in order to find the gradient of the tangent at the curve. Remember that when differentiating polynomials, we multiply the index of the vari...

The first step is to find dy/dx.

To do this you must first expand the brackets.

x² + y² + 2xy = xy²

Then differentiate each te...

Solve the equation x²=2x (solve x²-2x=0 by factorisation). Sketch the graphs y=x² and y=2x, using standard graph shapes. Look at the sketch to see for which values of x...

To factorise 3a³b + 12a²b² + 9a⁵b³, we need to deal with like elements together.Start with the integers. The highest common factor of 3, 12, and 9 is...

To do this, we first need to calculate the prime factorisations of 432 and 522, that is to say we need to break the numbers down into their prime factors.Let's start with 432. 432 = 2 x 216432 = 2 x ( 2 x...