Question

Describe the process of the difference of two squares. In your opinion what makes a difference of two squares easy to factor?
First, define a perfect square. Then, indicate what to look for to confirm that you have a difference of squares. Finally , give an example, possibly one where you need to factor out a GCF ( greatest common factor) before using a difference of squares.
How can we use difference of squares repeatedly to factor a difference of fourth powers such as x4 - 81?What about x8- 256?

Answer 1

solution. Process of difference of square Formula a²- 6² (atb) a-b) When of their square a and b are two numbers then difference will be quite easy to factor a_b² = (a+b) (arb) Because, (a+b) (a-b) a (a-b) + bla-b) = a²-ax+be-b2 az_b2 Perfect Square A perfect Square are whole numbers square of lice 1, 4, 9, 16, are the perfect speare of 1, 2, 3, 4, 5 respectively Example 25 - 9 This can be solved also ay 25-9 (5)²-(3)2 = (5+3) (5-2) = 8x2=16 Let, Take an Expression of a (x-2)(x+6) (2²-36) (x²-y) to simplity (2-2) N+6) (Q²6²) (x²-2) ar) (+6) 0461 62-6) (x+2382) MF6)(x+2)

For او با ) (22) - (0) 2 (و + 2ع) (و-x2) د (2 +ع) (32 - 2ع) « =) (22+3) (2-3) (2-3) (+9) (+3) (3) /8 - که ,مهم 2 - 256 2 2 (8) - 2 (ع) 2 =) (x - ) ( ) (1+) (*ري - )) * ) (2 -۶) (۶) (۶۶) ) - (2-2) (22+۶) (۲ + () (/۶) (۶+ع) (2-> (42) و Hence, اک - 9د (+) (+) (2) (2)