10 POINTS MATH QUESTIONS?!?!?!?

Question

Find the number that should be added to each expression to change it into a perfect square trinomial. Then write the expression as a perfect square trinomial
1. x^2 + 6x
2. x^2 - 8x
3. x^2 - 7x

Answer 1

1) x^2+6x

x^2+2*3*x

Compare with perfect square (a+b)^2 = a^2+2ab+b^2

a=x, b =3

b^2 = 3^2 =3*3 = 9

So 9 should be added to x^2+6x

x^2+6x+9 is perfect square trinomial.

2) x^2-8x

x^2-2*4*x

Compare with perfect square (a-b)^2 = a^2-2ab+b^2

a= x,b = 4

b^2 = 4^2 = 4*4 =16

So 16 should be added to x^2-8x

x^2-8x+16 is perfect square trinomial.

3) x^2-7x 

x^2-2*7/2*x

Compare with perfect square (a-b)^2 = a^2-2ab+b^2

a = x,b = 7/2

b^2 = 7/2*7/2 = 49/4

So 49/4 should be added to x^2-7x

x^2-7x+49/4 is perfect trinomial.