Question

a^4+4b^4+3a^2b^2. factorize​

Answer 1

Answer: a4-3a2b2-4b4  

Final result :

 (a2 + b2) • (a + 2b) • (a - 2b)

Step by step solution :

Step  1  :

Equation at the end of step  1  :

 ((a4)-((3•(a2))•(b2)))-22b4

Step  2  :

Equation at the end of step  2  :

 ((a4) -  (3a2 • b2)) -  22b4

Step  3  :

Trying to factor a multi variable polynomial :

3.1    Factoring    a4 - 3a2b2 - 4b4  

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

Found a factorization  :  (a2 + b2)•(a2 - 4b2)

Trying to factor as a Difference of Squares :

3.2      Factoring:  a2-4b2  

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.

Step-by-step explanation:

Answer 2

Answer:

(a² + b²)(a + 2b)(a - 2b)

Step-by-step explanation:

a^4+4b^4+3a^2b^2

= [(a^4){(3(a2²)(b²)}]-22b^4

= [(a^4)-(3a²b²)]-22b^4

= a^4-3a²b²- 4b^4

= (a² + b²)(a² - 4b²)

= a²-4b²

= (a + 2b)(a - 2b)

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