Question

factorization
15625a^6-64b^6​

Answer 1

Answer:

Ans:- (25a^2-4b^2)(125a^4+16b^4+100a^2b^2)

Step-by-step explanation:

15625a^6-64b^6

=(25a^2)^3-(4b^2)^3

=(25a^2-4b^2)(125a^4+16b^4+25a^2×4b^2). [a^3-b^3=(a-b)(a^2+b^2+ab)]

=(25a^2-4b^2)(125a^4+16b^4+100a^2b^2)

Hope this helps...

Answer 2

Answer:

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 : a6 is the square of a3

Check : b6 is the square of b3

Factorization is : (a3 + 8b3) • (a3 - 8b3)

Trying to factor as a Sum of Cubes :

2.2 Factoring: a3 + 8b3

Theory : A sum of two perfect cubes, a3 + b3 can be factored into :

(a+b) • (a2-ab+b2)

Proof : (a+b) • (a2-ab+b2) =

a3-a2b+ab2+ba2-b2a+b3 =

a3+(a2b-ba2)+(ab2-b2a)+b3=

a3+0+0+b3=

a3+b3

Check : 8 is the cube of 2

Check : a3 is the cube of a1

Check : b3 is the cube of b1

Factorization is :

(a + 2b) • (a2 - 2ab + 4b2)

Trying to factor a multi variable polynomial :

2.3 Factoring a2 - 2ab + 4b2

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

Factorization fails

Step-by-step explanation:

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