document.write( "Question 1121716: FInd the x^2 term in the expansion of (2 +3x)^2(4x +1)^2 \n" ); document.write( "

Algebra.Com's Answer #737707 by greenestamps(13200) $\"\"$ $\"About$

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\n" ); document.write( "The answer by the other tutor has errors; perhaps he will see my response and fix his....

\n" ); document.write( "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.

\n" ); document.write( "The first squared expression expands to $\"4%2B12x%2B9x%5E2\"$ ; the second to $\"16x%5E2%2B8x%2B1\"$ .

\n" ); document.write( "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

\n" ); document.write( " $\"4%2816%29%2B12%288%29%2B9%281%29+=+64%2B96%2B9+=+169\"$

\n" ); document.write( "The x^2 term in the expansion is 169x^2. \n" ); document.write( "

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