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

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) (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) (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 ; the second to .

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

The x^2 term in the expansion is 169x^2.
RELATED QUESTIONS
Find the sixth term in the expansion of {{{ (3x^2 - 1/x)^9... (answered by ikleyn,MathTherapy)
Find the term in x^4 in the expansion of... (answered by Edwin McCravy)
without nesessary expanding find the term tha does not contain valiable x in the... (answered by Boreal,MathTherapy)
find the term independent of x in the expansion... (answered by stanbon)
find the constant term in the expansion of... (answered by greenestamps)
In the following expansion,find the indicated term. (1+2x^2)^8 ,term in... (answered by MathLover1)
Binomial theorem: Find the term independent of x in the expansion of (1+x^6)(x^-2-3x)^9... (answered by stanbon)
Find the constant term (x^0) in the expansion of: {{{ (1 - x^2 + x^3)... (answered by greenestamps)
Find the fourth term in the expansion of... (answered by Alan3354)