6) $$ 12 a^{2}+23 a b+10 b^{2} $$

Question

UpStudy AI · Accepted Answer

To factor the quadratic expression $$12a^{2} + 23ab + 10b^{2}$$, follow these steps:

1. **Identify the Coefficients:**
   - $$ A = 12 $$ (coefficient of $$a^2$$)
   - $$ B = 23 $$ (coefficient of $$ab$$)
   - $$ C = 10 $$ (coefficient of $$b^2$$)

2. **Find Two Numbers That Multiply to $$ A \times C = 120 $$ and Add to $$ B = 23 $$:**
   - The numbers are **8** and **15** since $$8 \times 15 = 120$$ and $$8 + 15 = 23$$.

3. **Rewrite the Middle Term Using These Numbers:**
   $$
   12a^{2} + 8ab + 15ab + 10b^{2}
   $$

4. **Factor by Grouping:**
   $$
   (12a^{2} + 8ab) + (15ab + 10b^{2}) \
   = 4a(3a + 2b) + 5b(3a + 2b)
   $$

5. **Factor Out the Common Binomial Factor:**
   $$
   (4a + 5b)(3a + 2b)
   $$

**Final Factored Form:**
$$
12a^{2} + 23ab + 10b^{2} = (4a + 5b)(3a + 2b)
$$

**Answer:**  
After factoring, the expression is (4a + 5b) multiplied by (3a + 2b):
(4a+5b)(3a+2b)
The factored form of $$12a^{2} + 23ab + 10b^{2}$$ is $$(4a + 5b)(3a + 2b)$$.

6) \( 12 a^{2}+23 a b+10 b^{2} \)

Real Tutor Solution

Answer

Solution

Bonus Knowledge

Related Questions

Latest Algebra Questions