Question

fatorize : 8 a^3- b^3 -4a^2 - b2 +4ab​

Answer 1

Step-by-step explanation:

STEP

1

:

Equation at the end of step 1

(((8•(a3))•(b2))-((44•(a2))•(b2)))-(22•3•7ab2)

STEP

2

:

Equation at the end of step

2

:

(((8•(a3))•(b2))-((22•11a2)•b2))-(22•3•7ab2)

STEP

3

:

Equation at the end of step

3

:

((23a3 • b2) - (22•11a2b2)) - (22•3•7ab2)

STEP

4

:

STEP

5

:

Pulling out like terms

5.1 Pull out like factors :

8a3b2 - 44a2b2 - 84ab2 = 4ab2 • (2a2 - 11a - 21)

Trying to factor by splitting the middle term

5.2 Factoring 2a2 - 11a - 21

The first term is, 2a2 its coefficient is 2 .

The middle term is, -11a its coefficient is -11 .

The last term, "the constant", is -21

Step-1 : Multiply the coefficient of the first term by the constant 2 • -21 = -42

Step-2 : Find two factors of -42 whose sum equals the coefficient of the middle term, which is -11 .

-42 + 1 = -41

-21 + 2 = -19

-14 + 3 = -11 That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -14 and 3

2a2 - 14a + 3a - 21

Step-4 : Add up the first 2 terms, pulling out like factors :

2a • (a-7)

Add up the last 2 terms, pulling out common factors :

3 • (a-7)

Step-5 : Add up the four terms of step 4 :

(2a+3) • (a-7)

Which is the desired factorization

Final result :

4ab2 • (a - 7) • (2a + 3)