Expanding the expression $(x+7)^2$ using the binomial theorem:

$(a+b)^2 = a^2 + 2ab + b^2$

Let $a = x$ and $b = 7$:

$(x+7)^2 = x^2 + 2(x)(7) + 7^2$

$= x^2 + 14x + 49$

So, the expanded form is:

$x^2 + 14x + 49$

Would you like a breakdown of the binomial expansion?

Related Questions:

1. How do you expand $(x - 5)^2$?
2. What is the general formula for $(a + b)^n$?
3. How can we factorize $x^2 + 14x + 49$ back into its original form?
4. How does this relate to the perfect square trinomial formula?
5. What happens if we expand $(2x+3)^2$?

Tip:

The square of a binomial always results in a trinomial where the middle term is twice the product of the two terms in the binomial.