Question

Study the products shown. Is there a pattern?

(x + 3)2 = x2 + 6x + 9

(x + 4)2 = x2 + 8x + 16

(x + 5)2 = x2 + 10x + 25

(x + 6)2 = x2 + 12x + 36

Each product is in the form ax2 + bx + c.

Which of the following describes the relationship between b and c?

c is 1.5 times that of b.

c is double b.

c is the square of half of b.

c is the square of b.

Answer 1

c is the square of half of b.

This is evident in all products,

(6/2)² = 3²
= 9
(8/2)² = 4²
= 16
(10/2)² = 5²
= 25
(12/2)² = 6²
= 36
(b/2)² = c

Answer 2

Answer:

The correct option is 3. c is the square of half of b.

Step-by-step explanation:

The given equations are

$(x+3)^2=x^2+6x+9$

$(x+4)^2=x^2+8x+16$

$(x+5)^2=x^2+10x+25$

$(x+6)^2=x^2+12x+36$

These are the perfect square. According to this pattern,

$(x+y)^2=x^2+2xy+y^2$           .... (1)

Each product is in the form

$(x+y)^2=ax^2+bx+c$         .... (2)

From (1) and (2), we get

$b=2y$

$c=y^2$

$c=(\frac{b}{2})^2$                    $[\because b=2y]$

It means c is the square of half of b.

Therefore the correct option is 3.