The given problem asks to simplify $(9x^2 + 7)^2$. Let's work through it step by step using the binomial expansion formula.

Formula:

For any binomial $(a + b)^2$, the expansion is: $(a + b)^2 = a^2 + 2ab + b^2$

Given:

$(9x^2 + 7)^2$

Here, $a = 9x^2$ and $b = 7$.

Step 1: Square the first term ($a^2$):

$a^2 = (9x^2)^2 = 81x^4$

Step 2: Multiply the two terms and double the result ($2ab$):

$2ab = 2 \cdot (9x^2) \cdot 7 = 2 \cdot 63x^2 = 126x^2$

Step 3: Square the second term ($b^2$):

$b^2 = 7^2 = 49$

Step 4: Combine the results:

$(9x^2 + 7)^2 = 81x^4 + 126x^2 + 49$

Final Answer:

$(9x^2 + 7)^2 = 81x^4 + 126x^2 + 49$

Would you like further clarification or help with similar problems?

5 Related Questions:

1. What is the expansion of $(2x + 5)^2$?
2. How do you factor a quadratic expression like $x^2 + 10x + 25$?
3. What is the formula for expanding $(a - b)^2$?
4. How would you expand $(4x^3 + 2)^2$?
5. Can you simplify $(3x + 7)(3x - 7)$ using the difference of squares?

Tip:

When expanding a square of a binomial, carefully square each term and include the cross product term $2ab$ to avoid errors.