Resolve the following into factors. 1. $$ x^{2} y+x y^{2} $$ 3. $$ a^{3} b+a b^{3} $$ 5. $$ \quad 3 x^{3} y^{3}-\frac{3 x^{2} y^{2}}{4} $$

Question

UpStudy AI · Accepted Answer

Let's factor each expression step by step:

### 1. $$ x^{2} y + x y^{2} $$

**Step 1:** Identify the common factor in both terms.
- The common factor is $$ x y $$.

**Step 2:** Factor out $$ x y $$.
$$
x^{2} y + x y^{2} = x y (x + y)
$$

**Factored Form:**
$$
x y (x + y)
$$

### 3. $$ a^{3} b + a b^{3} $$

**Step 1:** Identify the common factor in both terms.
- The common factor is $$ a b $$.

**Step 2:** Factor out $$ a b $$.
$$
a^{3} b + a b^{3} = a b (a^{2} + b^{2})
$$

**Factored Form:**
$$
a b (a^{2} + b^{2})
$$

### 5. $$ 3 x^{3} y^{3} - \frac{3 x^{2} y^{2}}{4} $$

**Step 1:** Identify the greatest common factor (GCF) in both terms.
- The GCF is $$ 3 x^{2} y^{2} $$.

**Step 2:** Factor out $$ 3 x^{2} y^{2} $$.
$$
3 x^{3} y^{3} - \frac{3 x^{2} y^{2}}{4} = 3 x^{2} y^{2} \left( x y - \frac{1}{4} \right)
$$

**Factored Form:**
$$
3 x^{2} y^{2} \left( x y - \frac{1}{4} \right)
$$

---

**Summary of Factored Forms:**

1. $$ x^{2} y + x y^{2} = x y (x + y) $$

3. $$ a^{3} b + a b^{3} = a b (a^{2} + b^{2}) $$

5. $$ 3 x^{3} y^{3} - \frac{3 x^{2} y^{2}}{4} = 3 x^{2} y^{2} \left( x y - \frac{1}{4} \right) $$
1. $$ x^{2} y + x y^{2} = x y (x + y) $$ 3. $$ a^{3} b + a b^{3} = a b (a^{2} + b^{2}) $$ 5. $$ 3 x^{3} y^{3} - \frac{3 x^{2} y^{2}}{4} = 3 x^{2} y^{2} \left( x y - \frac{1}{4} \right) $$

Resolve the following into factors. 1. \( x^{2} y+x y^{2} \) 3. \( a^{3} b+a b^{3} \) 5. \( \quad 3 x^{3} y^{3}-\frac{3 x^{2} y^{2}}{4} \)

Real Tutor Solution

Answer

Solution

Beyond the Answer

Related Questions

Latest Algebra Questions