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Step 1:I'll solve this problem step by step, following the LaTeX formatting guidelines precisely:
Step 2:: Identify the Problem
We need to expand the expression $$(x+4)^{2}$$ using the binomial expansion.
Step 3:: Recall the Binomial Expansion Formula
The general form for squaring a binomial $$(a+b)^{2}$$ is:
$(a+b)^{2} = a^{2} + 2ab + b^{2}
Step 4:: Apply the Formula to Our Specific Problem
(x+4)^{2} = x^{2} + 2(x)(4) + 4^{2}
Substituting these values:
Step 5:: Simplify the Expansion
= x^{2} + 2(4x) + 16
= x^{2} + 8x + 16
Final Answer
Key Insights: - The expansion follows the $(a+b)^{2} = a^{2} + 2ab + b^{2}$ pattern - Each term is simplified systematically - The result is a quadratic expression in standard form
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