Question

add the term that makes the given expression into a perfect square. write the result as the square of a bracketed expression c square - 4c​

Answer 1

Perfect Squares

Perfect square formula/rules:

• 
  `a^2+2ab+b^2=(a+b)^2`
• 
  `a^2-2ab+b^2=(a-b)^2`

Trinomials are often organized like
`ax^2+bx+c`.

The b value in this case is c, and it will always equal the square of half of the b value.

• Perfect square trinomial:
  `ax^2+bx+((b)/(2))^2`
• or
  `ax^2-bx+((b)/(2))^2`

Solving the Question

We're given:

• 
  `c^2-4c`

In a trinomial, we're given the
`ax^2` and
`bx` values. a in this case is 1 and b in this case is 4. To find the third value by dividing 4 by 2 and squaring the quotient:

• 4 ÷ 2 = 2
• 2² = 4

Therefore, the term that we can add is + 4.

`c^2-4c+4`

To write this as the square of a bracketed expression, we can follow the rule
`a^2-2ab+b^2=(a-b)^2`:

`(c-2)^2`

Answer

`c^2-4c+4`

`(c-2)^2`