Question

(a + 1)(a + 8) = 0 How to solve

Answer 1

Answer:Since both terms are perfect cubes, factor using the difference of cubes formula,

a

3

−

b

3

=

(

a

−

b

)

(

a

2

+

a

b

+

b

2

)

where

a

=

x

and

b

=

2

.

(

x

−

2

)

(

x

2

+

x

⋅

2

+

2

2

)

=

0

Simplify.

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(

x

−

2

)

(

x

2

+

2

x

+

4

)

=

0

If any individual factor on the left side of the equation is equal to

0

, the entire expression will be equal to

0

.

x

−

2

=

0

x

2

+

2

x

+

4

=

0

Set the first factor equal to

0

and solve.

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x

=

2

Set the next factor equal to

0

and solve.

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x

=

−

1

+

i

√

3

,

−

1

−

i

√

3

The final solution is all the values that make

(

x

−

2

)

(

x

2

+

2

x

+

4

)

=

0

true.

x

=

2

,

−

1

+

i

√

3

,

−

1

−

i

√

3

Step-by-step explanation:

Answer 2

(a + 1) (a + 8) = 0

a^2 + 8a + a + 8 = 0
a^2 + 9a + 8 = 0
a^2 + a + 8a + 8 = 0
a (a + 1) + 8 (a + 1) = 0
(a + 1) (a + 8) = 0

a + 1 = 0
a = -1

a + 8 = 0
a = -8