Factorize:
ab2(Square)-ac2 (square),hence show that 10x(5.5)-10 (4.5)2 (square)=100
a b^2 - a c^2 ???????
a(b+c)(b-c)
10(5.5+4.5)(5.5-4.5)
10(10)(1) =
To factorize the expression ab^2 - ac^2, we can use the difference of squares pattern. The difference of squares states that a^2 - b^2 can be factored as (a + b)(a - b).
In our case, we have ab^2 - ac^2. We can rewrite it as a(b^2 - c^2). Now, we can factorize b^2 - c^2 using the difference of squares pattern. It becomes (b + c)(b - c).
The factorized form of ab^2 - ac^2 is a(b + c)(b - c).
Now let's use this factorization to solve the equation 10x(5.5) - 10(4.5)^2 = 100:
Step 1: Replace the variables with their respective values.
10x(5.5) - 10(4.5)^2 = 100
Step 2: Simplify the expression within the parentheses.
10x(5.5) - 10(20.25) = 100
Step 3: Square the number inside the parentheses.
10x(5.5) - 10(410.0625) = 100
Step 4: Multiply the remaining numbers and simplify.
55x - 4100.625 = 100
Step 5: Move the constant term to the other side of the equation.
55x = 100 + 4100.625
Step 6: Add the constants.
55x = 4200.625
Step 7: Divide both sides by 55 to solve for x.
x = 4200.625 / 55
x ≈ 76.375
So, the value of x which satisfies the equation is approximately 76.375.