Question

Simplify (x² + x +1 ) ( x²-x +1)​

Answer 1

Answer:

Step-by-step explanation:

We must ensure that each term in the second bracket is multiplied by each term in the first bracket.

This can be done as follows.

(

x

2

+

x

−

1

)

(

x

+

1

)

=

x

2

(

x

+

1

)

+

x

(

x

+

1

)

−

1

(

x

+

1

)

distribute each set of brackets.

=

x

3

+

x

2

+

x

2

+

x

−

x

−

1

and now collect like terms

⇒

x

3

+

x

2

+

x

2

+

x

−

x

−

1

=

x

3

+

2

x

2

−

1

=

x

3

+

2

x

2

−

1

in standard form

Standard form means writing the expression beginning with the term which has the highest power of the variable. In this case

x

3

then the next term with the next highest power. In this case

+

2

x

2

and so on until the last term.