Question

(b+2)(b^2b+4)-b(b^2-1)при b = -2/3

Answer 1

B^3+b^2+4b+2b^2+4b+8-b^3+b=3b^2+9b+8=4/3-6+8=4/3+2=2 4/3

Answer 2

To evaluate the expression (b+2)(b^2b+4)-b(b^2-1) at b = -2/3, we substitute -2/3 in place of b and perform the calculations.

Let's start with the given expression:

(b+2)(b^2b+4)-b(b^2-1)

Substituting b = -2/3:

((-2/3)+2)((-2/3)^2(-2/3)+4)-(-2/3)((-2/3)^2-1)

Simplifying further:

((-2/3)+2)((4/9)(-2/3)+4)-(-2/3)((4/9)-1)

((-2/3)+2)((-8/27)+4)-(-2/3)((4/9)-1)

((-2/3)+2)(-8/27+4)-(-2/3)(4/9-1)

((-2/3)+2)(-8/27+4)-(-2/3)(4/9-9/9)

((-2/3)+2)(-8/27+4)-(-2/3)(-5/9)

((-2/3)+2)(-8/27+4)+(2/3)(5/9)

((-2/3)+2)(116/27)+(10/27)

Now we can simplify the expression further:

((-2/3)+2)(116/27)+(10/27)

((-2/3)+(6/3))(116/27)+(10/27)

(4/3)(116/27)+(10/27)

(4/3)*(116/27)+(10/27)

(464/81)+(10/27)

(464/81)*(9/9)+(10/27)

(4649)/(819)+(10/27)

4176/729+10/27

Multiply both fractions by a common denominator:

(4176/729)*(27/27)+(10/27)

(417627)/(72927)+(10/27)

112,752/19,683+10/27

Now, we can find a common denominator for the fractions:

(112,752+10729)/(19,68327)

(112,752+7,290)/(19,683*27)

120,042/531,261

Therefore, the value of the expression (b+2)(b^2b+4)-b(b^2-1) at b = -2/3 is approximately 0.2257.