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: $ax^2+bx+(\dfrac{b}{2})^2$
• or $ax^2-bx+(\dfrac{b}{2})^2$

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

$c^2-4c+4$

$(c-2)^2$