Q. \((x+5)^2\)
Answer
Use the binomial square formula: \( (a+b)^2=a^2+2ab+b^2 \). Here \(a=x\) and \(b=5\).
\[
(x+5)^2=x^2+2(x)(5)+5^2=x^2+10x+25
\]
Detailed Explanation
We want to expand the expression \( (x+5)^2 \) step by step.
Step 1: Use the square of a binomial rule.
For any numbers \(a\) and \(b\), the identity is:
\[
(a+b)^2 = a^2 + 2ab + b^2
\]
Step 2: Identify \(a\) and \(b\).
In \( (x+5)^2 \), we have \(a=x\) and \(b=5\).
Step 3: Substitute into the formula.
\[
(x+5)^2 = x^2 + 2(x)(5) + 5^2
\]
Step 4: Simplify each term.
Compute the middle term first:
\[
2(x)(5) = 10x
\]
Compute the last term:
\[
5^2 = 25
\]
Now the expression becomes:
\[
(x+5)^2 = x^2 + 10x + 25
\]
Final Answer:
\[
(x+5)^2 = x^2 + 10x + 25
\]
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Algebra FAQ
Expand \( (x+5)^2 \)?
\( (x+5)^2 = x^2 + 10x + 25 \).
What are the square and cross terms in \( (x+5)^2 \)?
Square terms: \(x^2\) and \(25\). Cross term: \(2\cdot x \cdot 5 = 10x\). So \(x^2+10x+25\).
How do you use the identity \( (a+b)^2 \)?
Use \( (a+b)^2 = a^2 + 2ab + b^2 \). Here \(a=x, b=5\): \(x^2 + 2(x)(5) + 5^2 = x^2+10x+25\).
What is the coefficient of \(x\) in \( (x+5)^2 \)?
The \(x\)-term is \(10x\), so the coefficient of \(x\) is \(10\).
What is the constant term of \( (x+5)^2 \)?
The constant term comes from \(5^2\), so it is \(25\).
Can you rewrite \( (x+5)^2 \) in standard quadratic form \(ax^2+bx+c\)?
Yes. \( (x+5)^2 = x^2 + 10x + 25 \), so \(a=1, b=10, c=25\).
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