How do you square binomials? for example: - 2n (2n+1) + (n+2) 2

The simplified form of this question is - 3n² + 2n + 4

Step-by-step explanation:

The first term - 2n (2n+1) simplifies to - 4n² - 2n through distributive property

The second term (n + 2) ² simplifies to n² + 4n + 4

When squaring binomials in form of (a + b) ², you can expand and use F. O. I. L.

(a + b) ² = (a + b) (a + b)

FOIL stands for

Firsts (The first term in each set of parenthesis)

Outsides (The outer most terms, or the first term in the first parenthesis,

and the second term in the second parenthesis)

Insides (The inner most terms, or the second term in the first

parenthesis and the first term in the second parenthesis)

Lasts (the second term in each set of parenthesis)

This is the order in which you multiply the terms together.

So we follow the steps and get ...

Firsts: a²

Outsides: ab

Insides: ba

Lasts: b²

Putting them togther gives us ...

a² + ab + ba + b²

which simlifies to

a² + 2ab + b² (ba = ab, so there are 2 ab terms)

Applying this to the second term in the original question gives us ...

(n + 2) ² = (n + 2) (n + 2)

Now foil ...

Firsts: n²

Outsides: 2n

Insides: 2n

Lasts: 4

which simplifies to n² + 4n + 4

So - 2n (2n+1) + (n+2) ² simplifies to

-4n² - 2n + n² + 4n + 4 which further simplifies to

-3n² + 2n + 4