Answer: The third choice, (x-7)(x-7)
Step-by-step explanation:
[tex](x+49)(x+1)\\(x+7)(x+7)\\(x-7)(x-7)\\(x-49)(x-1)\\[/tex]
Given, [tex]x^2-14x+49[/tex]
Let's check the first one, 49x+x = 50x, not even right.
The second one, 7x+7x = 14x, it's wrong because it's -14x and not 14x
Third, -7x-7x = -14x which is right, (-7)(-7) = 49 which is right
Fourth, -49x-x = -50x not right.
Also for the second and third choices, you can convert it to perfect square
[tex](x+7)^2 \\(x-7)^2[/tex]
The formula of perfect square: [tex]ax^2+2(a)(b)(x)+b^2[/tex]
a = 1 and b = 7 so... From [tex](x+7)^2[/tex]
[tex]x^2+2(1)(7)(x)+7^2[/tex] = [tex]x^2+14x+49[/tex]
While (x-7)^2
[tex]x^2-2(1)(7)(x)+7^2 = x^2-14x+49[/tex]
So the answer is the third choice.
