What number should be added to the expression to turn it into a perfect square trinomial x^2+2x

Solutions

A Perfect Square Trinomial is the product of two binomials. Both the binomials are same. When you multiply an algebraic expression with two terms to itself, you will get a three-term expression called a perfect square trinomial. A perfect square trinomial is one that factors into two identical factors. The general forms of perfect square trinomial are =

(ax - b) ² = (ax) ² - 2axb + b ² and (ax + b) ² = (ax) ² + 2axb + b²

Calculations

αx²+βx+c

The variable α = 1 for ease

Take the variable b and half it then square that

to make c = number

x²+2x+c

variable α = 1

variable β = 2

2 : 2=1

1² = 1

x²+2x+1

(x+1) ²

In conclusion the number (1) should be added to the expression to turn it into a perfect square trinomial.

Kinda like completing the square

if you have

ax^2+bx+c

a=1 for ease

take b and halve it then square that

then make c = that

x^2+2x+c

a=1 good

b=2

2/2=1

1^2=1

x^2+2x+1

(x+1) ^2

the number 1 should be added