Question

factorise each of the following algebraic expression expressible as the sum of difference of two cubes 1) 8a^5 b^2+27a^2b^2​

Answer 1

Answer:

STEP

1

:

Equation at the end of step 1

((8•(a5))•(b2))+(33a2•b5)

STEP

2

:

Equation at the end of step

2

:

(23a5 • b2) + 33a2b5

STEP

3

:

STEP

4

:

Pulling out like terms

4.1 Pull out like factors :

8a5b2 + 27a2b5 = a2b2 • (8a3 + 27b3)

Trying to factor as a Sum of Cubes:

4.2 Factoring: 8a3 + 27b3

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 : 27 is the cube of 3

Check : a3 is the cube of a1

Check : b3 is the cube of b1

Factorization is :

(2a + 3b) • (4a2 - 6ab + 9b2)

Trying to factor a multi variable polynomial :

4.3 Factoring 4a2 - 6ab + 9b2

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

Factorization fails

Final result :

a2b2 • (2a + 3b) • (4a2 - 6ab + 9b2)

Step-by-step explanation:

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