Expand and simplify (x + 4)²
Understand the Problem
The question is asking to expand the expression (x + 4)² and then simplify the result. This involves applying the formula for the square of a binomial.
Answer
The expanded expression is $x^2 + 8x + 16$.
Answer for screen readers
The expanded and simplified expression is:
$$x^2 + 8x + 16$$
Steps to Solve
- Apply the binomial square formula
To expand the expression $(x + 4)^2$, we will use the formula for the square of a binomial:
$$(a + b)^2 = a^2 + 2ab + b^2$$
Here, $a = x$ and $b = 4$.
- Substitute values into the formula
Substituting $a$ and $b$ into the formula gives us:
$$(x + 4)^2 = x^2 + 2(x)(4) + 4^2$$
- Calculate each term
Now, calculate each of the terms:
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First term: $x^2$ remains $x^2$.
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Second term: $2(x)(4) = 8x$.
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Third term: $4^2 = 16$.
Putting this all together:
$$(x + 4)^2 = x^2 + 8x + 16$$
- Write the final expression
Now, we simplify the expression:
The final result is:
$$x^2 + 8x + 16$$
The expanded and simplified expression is:
$$x^2 + 8x + 16$$
More Information
The expression $(x + 4)^2$ represents the area of a square with a side length of $(x + 4)$, which is useful in geometry and algebra. This expansion finds usage in many areas including solving quadratic equations and factoring.
Tips
- Forgetting to apply the formula correctly: Some may expand $(x + 4)(x + 4)$ directly without using the binomial square formula, missing the intermediate steps.
- Miscalculating coefficients: Make sure to multiply the coefficients correctly, especially in the $2ab$ term.
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