Solve (a) (r - 9u)² (b) 4(a + b)(a - 2b)(b - a) Simplify (a) -12 (m+9) = 396 (b) 6u - 18 = 8u/40 - 3½ (c) 8c - 100 = -14c + 308
a) (r-9u)^2=r^2 - 2*9u*r + (9u)^2=
=(r^2)-18*(u*r) + 81*(u^2)
I have to metion that it was used the formula
(a-b)^2=a^2 - 2*a*b - b^2
b) For solving this relation, we have to re-write it, based on the property of commutativity of adding relation, so that (a+b) could be written as (b+a). The relation will become:
In this way, we could note that we have the development of squares difference: (b+a)*(b-a)=(b)^2-(a)^2
We'll open the parenthesis and we'll have:
We'll divide with (-12), the relation above:
First of all, we note that "8u/40" could be written as "8u/8*5", in order to simplify 8. The result will be "u/5".
Second of all, we'll write the terms with "u" in the left side of equal and the free terms on the right side:
We'll find out the same denominator on the left side, which is 5, and we'll amplify "6u" with 5.
We'll find out the same denominator on the right side, which is 2, and we'll amplify "18" with 2.
We could divide the relation with "29"
We'll cross multiplying:
As we've did at the point b), we'll write the terms with "u" in the left side of equal and the free terms on the right side:
We could simplify with 2, because both 22 and 204 are divisible by 2:
We use (a+b)^2=a^2+2ab+b^2 and expand the expression(r-9u)^2
a=r and b=-9u. Therefore(r-9u)^2=a^2-2r*(-u)+(-9u)^2= a^2-18au+81u^2.
4(a+b)(a-2b)((b-a) could be written like:-4(a+b)(a-2b)((a-b)
We Use, the identity ,(x+l)(x+m)(x+n)=x^3+(l+m+n)x^2+(lm+mn+cnl)x+lmn, we get by putting x=a, l=b, m=-2b and n=-b, we get:
Simplifying and solving for the unkown:
-12 (m+9) = 396
Divide both sides by -12 and then subtract -9 from both sides to get m.
m+9 = 396/(-12)=-33
m= -33-9= -42
6u - 18 = 8u/40 - 3½
8u/40=0.2u and 3 1/2 = 3.5
We use the above ordinary decimal numbers, instead of fractions and rewrite the equation:
6u-18= 0.2u -3.5.
Collect the variables on left and numerals on the right by adding , -0.2u+18 to both sides:
Simplify both sides:
Simplify bith sides:
Divide both sides by 5.8:
8c - 100 = -14c + 308
Collect the variables on left and numbers, the known on the right, by adding 14c+100 to both sides of the equation and simplify:
Divide by 22 both sides: