SOLUTION: 7. Essay; show all work. Find the product: (1/4x^2-2/7)(-1/2x-1/2) please help.

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: 7. Essay; show all work. Find the product: (1/4x^2-2/7)(-1/2x-1/2) please help.       Log On


   

Question 499455: 7. Essay; show all work. Find the product:
(1/4x^2-2/7)(-1/2x-1/2)

please help.

Answer by oberobic(2304) About Me  (Show Source):
You can put this solution on YOUR website!
This is a very tedious problem, with lots of potential for mistakes.
.
+%28%281%2F4%29x%5E2-2%2F7%29%28-%281%2F2%29x-1%2F2%29+
.
Let:
+s+=+%281%2F4%29%2Ax%5E2+
+t+=+2%2F7+
+u+=+-%281%2F2%29%2Ax+
+v+=+1%2F2+
.
Substitute
+%28s-t%29%28u-v%29+
.
Use FOIL to define terms
.
+s%2Au+-+s%2Av+-+t%2Au+%2B+t%2Av+
.
Now substitute for s, t, u & v
.

.
Rearrange the multiplications since their order does not affect values
.

.
Simplify
.
-%281%2F8%29%2Ax%5E3+-+%281%2F8%29%2Ax%5E2+%2B+%282%2F14%29%2Ax+%2B+2%2F14
.
multiply through by 112 to eliminate fractions
.
-14x%5E3+-+14x%5E2+%2B16x+%2B+16
.
divide through by 2
-7x%5E3+-7x%5E2+%2B8x+%2B+8
.
graph%28500%2C500%2C-3%2C3%2C-10%2C10%2C-7%2Ax%5E3+-+7%2Ax%5E2+%2B8%2Ax+%2B+8%29