Description
This formula shows how to factor the sum of two fifth powers.
Example
Example 1:| $(a-2)^2 = a^2 - 2\cdot a \cdot 2 + 2^2 = a^2 - 4a + 4$ Example 2:| $A (3x-5y)^2 &= (3x)^2 - 2 \cdot 3x \cdot 5y + (5y)^2\\ &= 9x^2 - 30xy + 25y^2 A$
Variables:
We use this formula to factor expressions of the form $a^2-b^2$.
Example 1:| $9a^2 - 4b^2 = (3a)^2-(2b)^2=(3a+2b)(3a-2b)$| Example 2:| $102^2-4 = 102^2-2^2=(102+2)(102-2)=104 \cdot 100=10400$| Example 3:| $102 \cdot 98 = (100+2)(100-2)=100^2-2^2 = 10000-4 = 9996$