Which expression shows the correct multiplication of the following polynomilas? 3x(6x^2-3x+7)

Mathematics

1 answer:

snow_tiger [21]3 years ago

8 0

Answer: 18x^3-9x^2+21x

Solution:

3x(6x^2-3x+7)=

Applying the distributive property in the multiplication to eliminate the parentheses:

(3x)(6x^2)+(3x)(-3x)+(3x)(7)=

(3*6)x^(1+2)+3*(-3)x^(1+1)+(3*7)x=

18x^3-9x^2+21x

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Answer: 17/18

In words, this is seventeen eighteenths

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Work Shown:

4/9 + 9/18

8/18 + 9/18 ... see note below

(8+9)/18

17/18

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note: To go from 4/9 to 8/18, we multiply top and bottom by 2. So that's why 4/9 = 8/18.

The diagram below shows a visual representation of why 4/9 = 8/18.

In the top row, I've drawn out 9 rectangles of the same size. Then I've shaded 4 of the 9 rectangles to represent the fraction 4/9. In the bottom row, I've cut each of those 9 rectangles into two smaller equal pieces, so we have 9*2 = 18 rectangles now. Note how the shaded regions are the same size, so this shows 4 green regions doubles to 2*4 = 8 yellow regions; therefore 4/9 is the same as 8/18.