Question

Determine which of the following are perfect square expressions. If so, factorise the expressions. (a) x2 + 4x + 4 (b) x2 + 18x + 36​

Answer 1

Step-by-step explanation:

a)x^2 +4x+4

x^2 +2x+2x+4

x(x+2)+2(x+2)

(x+2)(x+2)

b) x^2 +15x+36

x^2+12x+3x+36

x(x+12)+3(x+12)

(x+3)(x+12)

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Answer 2

Answer:

12 or -12

Step-by-step explanation:

Consider the equation

0=x2+4x+4

. We can solve this by factoring as a perfect square trinomial, so

0=(x+2)2→x=−2and_2

. Hence, there will be two identical solutions.

The discriminant of the quadratic equation (

b2−4ac) can be used to determine the number and the type of solutions. Since a quadratic equations roots are in fact its x intercepts, and a perfect square trinomial will have 2 equal, or 1

distinct solution, the vertex lies on the x axis. We can set the discriminant to 0 and solve:

k2−(4×1×36)=0k2−144=0(k+12)(k−12)=0k=±12

So, k can either be

12 or −12

.

Hopefully this helps!