Question

factorization a4+4b4​

Answer 1

Answer:

(a2 + 2b2) • (a2 - 2b2)

Step-by-step explanation:

Step by step solution :

Step 1 :

Equation at the end of step 1 :

(a4) - 22b4

Step 2 :

Trying to factor as a Difference of Squares :

2.1 Factoring: a4-4b4

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 : 4 is the square of 2

Check : a4 is the square of a2

Check : b4 is the square of b2

Factorization is : (a2 + 2b2) • (a2 - 2b2)

Trying to factor as a Difference of Squares :

2.2 Factoring: a2 - 2b2

Check : 2 is not a square !!

Ruling : Binomial can not be factored as the difference of two perfect squares.

Final result :

(a2 + 2b2) • (a2 - 2b2)

Answer 2

Answer:

$(a^2+2b^2i)(a^2-2b^2i)$

Step-by-step explanation:

$a^4+4b^4$ is not able to be factored over real numbers.

When $a^4+4b^4$ is factored over imaginary numbers,

$a^4+4b^4=(a^2+2b^2i)(a^2-2b^2i)$

Factoring is over.

∴$(a^2+2b^2i)(a^2-2b^2i)$