Answer:
The complete expression is [tex]x^2 + 8x + 16 [/tex]
So the missing term is 16.
Step-by-step explanation:
Here, the given expression is: [tex]x^2 + 8x + [/tex]
Let us assume the missing term = [tex]k^2[/tex]
So, the given expression becomes [tex]x^2 + 8x + k^2[/tex]
Now, by ALGEBRAIC IDENTITY:
[tex](a +b)^2 = a^2 + b^2 + 2ab[/tex]
So, here applying this identity, we get
[tex]a^2 + 2ab + b^2 = x^2 + 8x + k^2[/tex]
So on comparing, we get
[tex]a^2 = x^2, b^2 = k^2, 2 ab = 8x = 2 (x) (4)[/tex]
So, we get that 2 (x) (4) = 2 (a)(b)
⇒ a = x, b= 4
[tex]\implies (a+b)^2 = (x+4)^2[/tex]
So, the missing term is [tex]k^2 = b^2 = (4)^2 = 16[/tex]
Hence, the complete expression is [tex]x^2 + 8x + 16 [/tex]
Answer: x^2 + 8x + 16
Step-by-step explanation:
I did it on Edge and got it right!
