(10a-b)(10a+b)=

Solution for (10a-b)(10a+b)= equation:

Simplifying
(10a + -1b)(10a + b) = 0

Multiply (10a + -1b) * (10a + b)
(10a * (10a + b) + -1b * (10a + b)) = 0
((10a * 10a + b * 10a) + -1b * (10a + b)) = 0

Reorder the terms:
((10ab + 100a2) + -1b * (10a + b)) = 0
((10ab + 100a2) + -1b * (10a + b)) = 0
(10ab + 100a2 + (10a * -1b + b * -1b)) = 0
(10ab + 100a2 + (-10ab + -1b2)) = 0

Reorder the terms:
(10ab + -10ab + 100a2 + -1b2) = 0

Combine like terms: 10ab + -10ab = 0
(0 + 100a2 + -1b2) = 0
(100a2 + -1b2) = 0

Solving
100a2 + -1b2 = 0

Solving for variable 'a'.

Move all terms containing a to the left, all other terms to the right.

Add 'b2' to each side of the equation.
100a2 + -1b2 + b2 = 0 + b2

Combine like terms: -1b2 + b2 = 0
100a2 + 0 = 0 + b2
100a2 = 0 + b2
Remove the zero:
100a2 = b2

Divide each side by '100'.
a2 = 0.01b2

Simplifying
a2 = 0.01b2

Take the square root of each side:
a = {-0.1b, 0.1b}