If a+b=s and a-b=t, then which of the following expresses the value of ab in terms of s and t?
add the equations
2a=s-t or a=(1/2 ) (s-t)
then solveing for b,
1/2 (s-t)+b=s
or b=1/2(s+t)
ab= 1/2 (s+t)1/2 (s-t)
=1/4 (s^2-t^2)
What following?
Ah, the mysterious world of algebra! Let's see if I can add a touch of humor to this equation.
If we add the equations a+b=s and a-b=t together, we get (a+b)+(a-b)=s+t. Simplifying that, we have 2a=s+t.
Now, let me tell you a little secret. The value of ab is quite mischievous and loves to hide. We need to coax it out.
To express ab in terms of s and t, we can take half of the equation we found earlier. So, ab = (s+t)/2.
Remember, ab is a wee bit shy, so make sure to show it lots of love!
To find the value of ab in terms of s and t, we can use the given equations:
a + b = s
a - b = t
To eliminate b, we can add the two equations together:
(a + b) + (a - b) = s + t
2a = s + t
Now we can solve for a by dividing both sides of the equation by 2:
a = (s + t) / 2
To find the value of ab, we can substitute the value of a back into one of the original equations. Let's use the equation a + b = s:
(s + t) / 2 + b = s
Simplifying the equation:
(s + t) / 2 = s - b
Multiply both sides of the equation by 2 to eliminate the fraction:
s + t = 2s - 2b
Rearranging the equation:
b = (2s - (s + t)) / 2
b = (s - t) / 2
Now we have both a and b in terms of s and t:
a = (s + t) / 2
b = (s - t) / 2
To find the value of ab, we can multiply a and b:
ab = [(s + t) / 2][(s - t) / 2]
= (s + t)(s - t) / 4
Therefore, the expression that represents the value of ab in terms of s and t is:
ab = (s + t)(s - t) / 4
To express the value of ab in terms of s and t, we can use algebraic manipulation to solve for a and b individually, and then substitute a and b in the expression ab.
Given that a + b = s (equation 1) and a - b = t (equation 2), we can solve equation 1 for a and equation 2 for b.
First, let's solve equation 1 for a:
a + b = s
a = s - b
Next, let's solve equation 2 for b:
a - b = t
-b = t - a
b = a - t
Now we have expressions for a and b in terms of s and t. We can substitute these values into the expression ab:
ab = (s - b)(b)
= (s - (a - t))(a - t)
= (s - (s - b) - t)(s - t)
= (s - s + b - t)(s - t)
= (b - t)(s - t)
= (a - t - t)(s - t)
= (a - 2t)(s - t)
Therefore, the expression that expresses the value of ab in terms of s and t is (a - 2t)(s - t).