Question

factorisea^4+4b^4 - 5a^2b^2​

Answer 1

Answer:

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Step-by-step explanation:

STEP

1

:

Equation at the end of step 1

((a4)-((5•(a2))•(b2)))+22b4

STEP

2

:

Equation at the end of step

2

:

((a4) - (5a2 • b2)) + 22b4

STEP

3

:

Trying to factor a multi variable polynomial

3.1 Factoring a4 - 5a2b2 + 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-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:

3.3 Factoring: a2 - 4b2

Check : 4 is the square of 2

Check : a2 is the square of a1

Check : b2 is the square of b1

Factorization is : (a + 2b) • (a - 2b)

Final result :

(a + b) • (a - b) • (a + 2b) •

Answer 2

Step-by-step explanation:

explanation is given in pictures