Answer:
Completing the square we get: [tex](x-2)^2-(2)^2[/tex]
and factoring the term we get: [tex]x(x-4)[/tex]
Step-by-step explanation:
We need to complete the square for the expression [tex]x^2-4x[/tex]
For completing the square the expression would be of form [tex]a^2+2ab+b^2=(a+b)^2[/tex]
For given expression we have to add (2)^2 and subtract to make it complete the square.
[tex]x^2-2(x)(2)+(2)^2-(2)^2\\(x-2)^2-(2)^2[/tex]
Now, we have to factor the polynomial using formula [tex](a)^2-(b)^2=(a-b)(a+b)[/tex]
So, [tex](x-2)^2-(2)^2\\=(x-2-2)(x-2+2)\\=(x-4)(x-0)\\=x(x-4)[/tex]
Completing the square we get: [tex](x-2)^2-(2)^2[/tex]
and factoring the term we get: [tex]x(x-4)[/tex]
