Question

simplify- (a2+b2)(a2+a2)-(a2-b2)(a2-b2)​

Answer 1

Step-by-step explanation:

(a2+b2)(a2+a2)-(a2-b2)(a2-b2) 

Final result :

a4 + 4a2b2 - b4

Reformatting the input :

Changes made to your input should not affect the solution:

 (1): "b2"   was replaced by   "b^2".  7 more similar replacement(s).

Step by step solution :

Step  1  :

Trying to factor as a Difference of Squares :

 1.1      Factoring:  a2-b2 

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 :  a2  is the square of  a1 

Check :  b2  is the square of  b1 

Factorization is :       (a + b)  •  (a - b) 

Trying to factor as a Difference of Squares :

 1.2      Factoring:  a2 - b2 

Check :  a2  is the square of  a1 

Check :  b2  is the square of  b1 

Factorization is :       (a + b)  •  (a - b) 

Multiplying Exponential Expressions :

 1.3    Multiply  (a + b)  by  (a + b) 

The rule says : To multiply exponential expressions which have the same base, add up their exponents.

In our case, the common base is  (a+b)  and the exponents are :

          1 , as  (a+b)  is the same number as  (a+b)1 

 and   1 , as  (a+b)  is the same number as  (a+b)1 

The product is therefore,  (a+b)(1+1) = (a+b)2 

Evaluate an expression :

 1.4    Multiply  (a-b)  by  (a-b) 

The rule says : To multiply exponential expressions which have the same base, add up their exponents.

In our case, the common base is  (a-b)  and the exponents are :

          1 , as  (a-b)  is the same number as  (a-b)1 

 and   1 , as  (a-b)  is the same number as  (a-b)1 

The product is therefore,  (a-b)(1+1) = (a-b)2 

Equation at the end of step  1  :

(((a2)+(b2))•((a2)+(a2)))-(a+b)2•(a-b)2

Step  2  :

Equation at the end of step  2  :

2a2 • (a2 + b2) - (a + b)2 • (a - b)2

Step  3  :

 3.1    Evaluate :  (a+b)2   =  a2+2ab+b2   3.2    Evaluate :  (a-b)2   =  a2-2ab+b2 

Trying to factor a multi variable polynomial :

 3.3    Factoring    a4 + 4a2b2 - b4 

Try to factor this multi-variable trinomial using trial and error 

 Factorization fails

Final result :

a4 + 4a2b2 - b4