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Example 10:

   4(2x - 3)(5x + 1)    Once again, do the FOIL first, in one step:
= 4(10x2 - 13x - 3)
= 40x2 - 52x - 12


Example 11:

   -2(3x - 4)2
= -2(9x2 - 24x + 16)    [Use extra steps here if you need to]
= -18x2 + 48x - 32


Here's the same example with all the steps:

       -2(3x - 4)2
    = -2(3x - 4)(3x - 4)
    = -2(9x2 - 12x - 12x + 16)
    = -2(9x2 - 24x + 16)
    = -18x2 + 48x - 32


Example 12:

   2(x + 1)2 + 3(x - 4)2
We'll do both FOILs first:
= 2(x + 1)(x + 1) + 3(x - 4)(x - 4)
= 2(x2 + 2x + 1) + 3(x2 - 8x + 16)
Now simplify:
= 2x2 + 4x + 2 + 3x2 - 24x + 48
= 5x2 - 20x + 50


Save some work by doing the FOILs without rewriting them:

       2(x + 1)2 + 3(x - 4)2
    = 2(x2 + 2x + 1) + 3(x2 - 8x + 16)
    = 2x2 + 4x + 2 + 3x2 - 24x + 48
    = 5x2 - 20x + 50


Example 13:

   -2(4x - 1)(2x + 5) + 3(2x - 3)2
= -2(8x2 + 18x - 5) + 3(4x2 - 12x + 9)
= -16x2 - 36x + 10 + 12x2 - 36x + 27
= -4x2 - 72x + 37
Once again, write out the missing steps if you need to


Example 13:

This time we'll show every step

   6(4x - 3)2 - 5(2x - 1)2
= 6(4x - 3)(4x - 3) - 5(2x - 1)(2x - 1)
= 6(16x2 - 12x - 12x + 9) - 5(4x2 - 2x - 2x + 1)
= 6(16x2 - 24x + 9) - 5(4x2 - 4x + 1)
= 96x2 - 144x + 54 - 20x2 + 20x - 5
= 76x2 - 124x + 49


NOTE:
  • There are some places above where you probably needed to use a calculator, perhaps with 6x16 or 6x-24. But don't slow yourself down by having to use your calculator for every multiplication; you should have the times tables up to 12 x 12 memorized by now. If not, make that a priority.
    If you don't know the times tables by now, you will find the upcoming unit on factoring polynomials unneccessarily difficult.


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