SOLUTION: FInd the x^2 term in the expansion of (2 +3x)^2(4x +1)^2

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Question 1121716: FInd the x^2 term in the expansion of (2 +3x)^2(4x +1)^2
Found 2 solutions by Boreal, greenestamps:
Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
the first term expands to
4+6x+9x^2,
the second expands to 16x^2+8x+4
The product is
64x^2+32x+16+
96x^3+48x^2+24x+
144x^4+72x^3+36x^2
148x^2.

Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


The answer by the other tutor has errors; perhaps he will see my response and fix his....

It is a useful skill, in a problem like this, to be able to get the answer to the question (the x^2 term in the expansion) without performing the entire multiplication.

The first squared expression expands to 4%2B12x%2B9x%5E2; the second to 16x%5E2%2B8x%2B1.

The x^2 term in the final product will come from (1) the product of the constant in the first of these and the x^2 term in the second; (2) the product of the x terms in each; and (3) the product of the x^2 term in the first and the constant in the second. The coefficient is then

4%2816%29%2B12%288%29%2B9%281%29+=+64%2B96%2B9+=+169

The x^2 term in the expansion is 169x^2.