Question

how to factorise (x^2+64)

Answer 1

Trying to factor as a Difference of Squares :

 1.1      Factoring:  x2-64 

Theory : A difference of two perfect squares,  A2 - B2  can be factored into  (A+B) • (A-B)

Proof :  (A+B) • (A-B) =
         A2 - AB + BA - B2 =
         A2 - AB + AB - B2 = 
         A2 - B2

Note :  AB = BA is the commutative property of multiplication. 

Note :  - AB + AB equals zero and is therefore eliminated from the expression.

Check : 64 is the square of 8
Check :  x2  is the square of  x1 

Factorization is :       (x + 8)  •  (x - 8) 

Equation at the end of step  1  :

(x + 8) • (x - 8) = 0

Step  2  :

Theory - Roots of a product :

 2.1    A product of several terms equals zero. 

 When a product of two or more terms equals zero, then at least one of the terms must be zero. 

 We shall now solve each term = 0 separately 

 In other words, we are going to solve as many equations as there are terms in the product 

 Any solution of term = 0 solves product = 0 as well.

Solving a Single Variable Equation :

 2.2      Solve  :    x+8 = 0 

 Subtract  8  from both sides of the equation : 
                      x = -8 

Solving a Single Variable Equation :

 2.3      Solve  :    x-8 = 0 

 Add  8  to both sides of the equation : 
                      x = 8 

Two solutions were found :

 x = 8

 x = -8

Answer 2

(x^2+64)
=(x)^2+(8)^2  (its actually x whole sq. and 8 whole sq)
=(x+8)(x+8)
it may be ur answer.