2006-07-04 18:26:29 · 7 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
Imagine a square of side a+b+c. Its area is (a+b+c)^2.
Now go along one side of the square and mark three points so that you have three columns of width a, b, and c. Then go along a different (perpendicular) side and mark off a, b, and c so that you have three rows of height a, b, and c.
You will now have 9 sections in the square - one with sides a & a; one with sides b & b; one with sides c & c; two with sides a & b, two with sides b & c; and two with sides a & c.
Calculate their areas and add.
The resulting sum is equal to the area of the square, i.e., (a+b+c)^2.
2006-07-04 18:48:53 · answer #1 · answered by Sorcia 2 · 0⤊ 0⤋
No. It has to be done pictorially or geometrically. Algebraic procedures are not allowed.
Here's how to do it.
Imagine the side of a square whose length is a + b + c. Now,
(a + b + c)^2
will represent the area of the square.
Draw such a square. Now, can you break your square up into smaller squares and rectangles? Sure you can.
One square is a^2. One square is b^2. One is c^2.
Now express all the remaining areas in terms of ab, bc, and ac. You will see it comes out as you want it to.
2006-07-04 18:42:10 · answer #2 · answered by ? 6 · 0⤊ 0⤋
multiply it with itself and you will get the answer i.e. a^2 +b^2+c^2+2ab+2bc+2ca
2006-07-04 18:42:17 · answer #3 · answered by Anonymous · 0⤊ 0⤋
put numbers to the letters. (i.e. a-2, b-3, c-4) dont use 1 or 0 because they have exceptions.
2006-07-04 18:30:44 · answer #4 · answered by hpascare 2 · 0⤊ 0⤋
why don't you actually try to multiply it out?
2006-07-04 18:29:32 · answer #5 · answered by instantly_oatmeal 7 · 0⤊ 0⤋
do the math
2006-07-04 20:14:36 · answer #6 · answered by Anonymous · 0⤊ 0⤋
(a+b+c)(a+b+c)=a (a+b+c)+b(+b+c)+c(a+b+c)
resolve this .you can get the desired
2006-07-04 22:24:59 · answer #7 · answered by ? 2 · 0⤊ 0⤋