Subjects algebra

Binomial Expansion 45A336

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1. **State the problem:** You asked how we got the 4 inside the expansion of $(x - 2)^2$. 2. **Recall the binomial square formula:** $$(a - b)^2 = a^2 - 2ab + b^2$$ 3. **Apply the formula to $(x - 2)^2$:** Here, $a = x$ and $b = 2$. $$ (x - 2)^2 = x^2 - 2 \times x \times 2 + 2^2 $$ 4. **Calculate each term:** $$ x^2 - 4x + 4 $$ 5. **Explanation:** The last term $4$ comes from squaring $2$, i.e., $2^2 = 4$. So, the $4$ is the square of the number $2$ in the binomial expansion.