Question

moong (express your answer in scientific notation.) 2. simplify: ((x + y)^2) (x^2 + 2xy + y^2) 3. the nth power of a number (x) is (\frac{x^n}{}) 4. graph all solutions to the inequality: (-3 leq x < 5)

Explanation:

Step1: Verify the algebraic identity

Recall the square of sum identity: $(a+b)^2 = a^2 + 2ab + b^2$. Substitute $a=x$, $b=y$.
$$(x+y)^2 = x^2 + 2xy + y^2$$

Step2: Confirm the simplification

The given expression $x^2+2xy+y^2$ matches the expanded form of $(x+y)^2$, so they are equivalent.

Step3: Graph the inequality on number line

1. Locate $x=-3$ and $x=5$ on the number line.
2. Use closed dots at both points (since the inequality includes equality: $\leq$).
3. Shade the segment between $-3$ and $5$ to represent all values in this interval.

Answer:

1. $\boldsymbol{(x+y)^2}$ (or $\boldsymbol{x^2+2xy+y^2}$, as they are equivalent)
2. $\boldsymbol{x^n}$
3. (Graph description: Closed dots at $-3$ and $5$ on the number line, with the segment between them shaded.)