Multiplication example, Mathematics

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Example 

Multiply 3x5 + 4x3 + 2x - 1 and x4 + 2x2 + 4.

The product is given by

3x5 . (x4 + 2x2 + 4) + 4x3. (x4 + 2x2 + 4) + 2x .

(x4 + 2x2 + 4) - 1 . (x4 + 2x2 + 4)

= 3x5 . x4 + 3x5 . 2x2 + 3x5 . 4 + 4x3 . x4 + 4x3 .

2x2 + 4x3 . 4 + 2x . x4 + 2x . 2x2 + 2x . 4 - x4 - 2x2 - 4

To simplify the above we employ a rule which we will learn in laws of indices. It states that  xm . xn = xm+n

= 3x9 + 6x7 + 12x5 + 4x7 + 8x5 + 16x3 + 2x5 + 4x3 + 8x - x4 - 2x2 - 4  

Now we collect like terms and simplify them. We obtain 3x9 + 10x7 + 22x5 - x4 + 20x3 - 2x2 + 8x - 4.


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