You can put this solution on YOUR website! 3x^2 (4x^2 - 2x + 3)
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The purpose of this problem is to teach you a couple of rules about algebraic multiplication.
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These rules are that you multiply the leading numbers (called coefficients) and add the
exponents of the like variables. In this case there is only the variable x. And remember that
x^2 has an exponent of 2 and just plain x has a variable of 1.
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On to the multiplication.
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The 3x^2 multiplies each of the 3 terms in the parentheses.
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The first multiplication is 3x^2 times 4x^2. Multiply the 3 times the 4 to get 12. Then you
multiply x^2 times x^2 by just adding the exponents to get x^4. So the result of multiplying
3x^2 by 4x^2 is 12x^4.
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The second multiplication is 3x^2 times -2x. The -2x should be thought of as -2x^1.
Multiply the 3 times the -2 to get -6 and multiply the x^2 times x^1 by adding the exponents
of 2 and 1 to get x^3. So the combined multiplication results in -6x^3.
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Finally the last of the three multiplications is to multiply 3x^2 times +3. This time
all you need to do is multiply the 3 times the +3 to get 9 and the x^2 tags along to
make this answer +9x^2.
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Putting all 3 answers together gives you the combined answer of 12x^4 -6x^3 + 9x^2.
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Answer A is the correct answer.
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I hope this helps you to see how to work this problem and that you can see how to apply a
couple of basic rules of algebraic multiplication to get the answer. The important thing
here is to understand what is going on.
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