For this week, we recapped that:
For expansion =
a) (a+b)² = a²+2ab+b²
b) (a-b)² = a²-2ab+b²
c) (a+b)(a-b) = a²-b²
Note:
a²+b² is NOT equals to (a+b)²
a²+b is equal to (a+b)²-2ab
For Factorization -
c) via common factors
3a + 12 = 3(a+4)
b) via perfect square
a²+4a+4= (a)² + 2(a)(2)+(2)² = (a+2)²
a²-4a+4 = (a)² + 2(a)(-2)+(-2)²
= (a)² - 2(a)(2)+(-2)²
= (a-2)²
c) via trail and error
d) via grouping
px+py+qx+qy = p(x+y) q(x+y)
For this week, we have done these examples:
Example 01:
Note: Find the Pattern - ½ - ⅓ same as 1/x - 1/x+1
Example 03:
Note: Factorize & Simplify each fraction independently
*Take Note!
Steps for solving questions-
- Factorize the denominator of the fraction independently
- If there are two separate fractions, factorize each fraction it by itself
- Find the LCM of both the fractions
- Make the two fractions into one.
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