Write an expression for the sum of the squares of two consecutive integers. (Use x for the integer.)
1
Simplify that expression.
2
Sum=n^2+(n+1)^2 which can be simplified.
how do you simplify? thank you bobpursley
expand (n+1)^2, then add the first n^2
To write an expression for the sum of the squares of two consecutive integers, we can start by representing the first consecutive integer as "x". Since we are looking for consecutive integers, the second consecutive integer would be "x + 1".
So, the sum of the squares of two consecutive integers can be expressed as:
x^2 + (x + 1)^2
To simplify the expression, we need to expand and simplify the terms.
Expanding (x + 1)^2:
(x + 1)(x + 1) = x^2 + x + x + 1 = x^2 + 2x + 1
Now we can substitute this expanded expression into our original equation:
x^2 + (x + 1)^2 = x^2 + (x^2 + 2x + 1)
Next, we combine like terms:
x^2 + x^2 +2x + 1 = 2x^2 + 2x + 1
So, the simplified expression for the sum of the squares of two consecutive integers is 2x^2 + 2x + 1.