How can a binomial expansion be done without Pascal’s triangle.

Use combinations. If the power was to 7 multiply the first by 7C0 then 7C1 all the way to 7C7.

You could also do 1, 7, 7X6÷2! , 7X6X5÷3! and on until you get to 1 again.

If you have to expand a binomial expansion and you can use Pascal’s triangle, what do you do?

Split the equation into 2 parts.

Using the numbers of the triangle.(1,4,6,4,1) multiply the pascal number by the first part to the power of the question and by the second part to the power of 0. Then add the next pascal number multiplied by the two values with each power adding to the original power each time.

How is an inequality solved with a graph?

Make one side equal to 0.

Factories the other side and find the values of X. These are the X intercepts of your graph.

Plot the graph. If the equation is >0 then you want everything above the X axis. <0 means use what is below the X axis.