Question

Express (x + 5)^2 as a trinomial in standard form.

Answer 1

Answer:

Ste(x−5)2=x2−10x 25

step-by-step explanation:

The standard form of a polynomial in one variable is a sum of terms in decreasing order of degree.

For brevity, terms with negative coefficients are usually written as subtractions rather than adding the additive inverses. That is, we would write  

x

2

−

3

x

+

2

rather than  

x

2

+

(

−

3

)

x

+

2

In order to express  

(

x

−

5

)

2

in standard form, we need to multiply it out, combining terms of like degree. We can use the FOIL mnemonic to help:

(

x

−

5

)

2

=

(

x

−

5

)

(

x

−

5

)

(

x

−

5

)

2

=

First



(

x

)

(

x

)

+

Outside



(

x

)

(

−

5

)

+

Inside



(

−

5

)

(

x

)

+

Last



(

−

5

)

(

−

5

)

(

x

−

5

)

2

=

x

2

−

5

x

−

5

x

+

25

(

x

−

5

)

2

=

x

2

−

10

x

+

25

Alternatively, we can recognise a pattern and use it.

For example:

(

a

+

b

)

2

=

a

2

+

2

a

b

+

b

2

(

a

−

b

)

2

=

a

2

−

2

a

b

+

b

2

So we could take the second of these and put  

a

=

x

,  

b

=

5

to find:

(

x

−

5

)

2

=

x

2

−

2

(

x

)

(

5

)

+

5

2

(

x

−

5

)

2

=

x

2

−

10

x

+

25