Find the value of c that makes the expression a perfect square trinomial. Then write the expression as the square of a binomial

Question

Question 1. x2+10x+c

and

Question 2. y2-12y+c

Answer 1

we know the relationship between the coefficients b and c is as follows

c = (b/2)^2

Question 1

so for the first question (x^2) + 10x + c

the coefficient b equals 10

c = (10/2)^2 = (5)^2 = 25

to get the expression as the square of the binomial we have

x^2 + 10x + (b/2)^2 = (x + (b/2))^2

= ( x+5 )^2

Question 2

for the second question (y^2) - 12y + c

the coefficient b equals -12

c = (-12/2)^2 = (-6)^2 = 36

to get the expression as the square of the binomial we have

x^2 - 12x + (b/2)^2 = (x + (b/2))^2

= ( x - 6 )^2

Answer 2

c = (1/2 the coefficient of the x term) squared = 25 = c

square of a binomial is ((x+5)^2

for number 2, half -12 is -6, squared = 36 = c

binomial squared is (x-6)^2