Question
(7square root 39 - square root 26)(square root 143 - square root 6)
Answers
GPT-4o mini
To simplify the expression \((7\sqrt{39} - \sqrt{26})(\sqrt{143} - \sqrt{6})\), we can use the distributive property (also known as the FOIL method for binomials).
1. **Multiply each term in the first parentheses by each term in the second parentheses:**
\[
(7\sqrt{39})(\sqrt{143}) + (7\sqrt{39})(-\sqrt{6}) + (-\sqrt{26})(\sqrt{143}) + (-\sqrt{26})(-\sqrt{6})
\]
2. **Simplify each product step by step:**
- First term:
\[
7\sqrt{39} \cdot \sqrt{143} = 7\sqrt{39 \cdot 143} = 7\sqrt{5577}
\]
- Second term:
\[
7\sqrt{39} \cdot -\sqrt{6} = -7\sqrt{39 \cdot 6} = -7\sqrt{234}
\]
- Third term:
\[
-\sqrt{26} \cdot \sqrt{143} = -\sqrt{26 \cdot 143} = -\sqrt{3718}
\]
- Fourth term:
\[
-\sqrt{26} \cdot -\sqrt{6} = \sqrt{26 \cdot 6} = \sqrt{156} = 2\sqrt{39}
\]
3. **Combine all the terms:**
\[
7\sqrt{5577} - 7\sqrt{234} - \sqrt{3718} + 2\sqrt{39}
\]
So, the final result is:
\[
7\sqrt{5577} - 7\sqrt{234} - \sqrt{3718} + 2\sqrt{39}
\]
This is the simplified form of the original expression.
1. **Multiply each term in the first parentheses by each term in the second parentheses:**
\[
(7\sqrt{39})(\sqrt{143}) + (7\sqrt{39})(-\sqrt{6}) + (-\sqrt{26})(\sqrt{143}) + (-\sqrt{26})(-\sqrt{6})
\]
2. **Simplify each product step by step:**
- First term:
\[
7\sqrt{39} \cdot \sqrt{143} = 7\sqrt{39 \cdot 143} = 7\sqrt{5577}
\]
- Second term:
\[
7\sqrt{39} \cdot -\sqrt{6} = -7\sqrt{39 \cdot 6} = -7\sqrt{234}
\]
- Third term:
\[
-\sqrt{26} \cdot \sqrt{143} = -\sqrt{26 \cdot 143} = -\sqrt{3718}
\]
- Fourth term:
\[
-\sqrt{26} \cdot -\sqrt{6} = \sqrt{26 \cdot 6} = \sqrt{156} = 2\sqrt{39}
\]
3. **Combine all the terms:**
\[
7\sqrt{5577} - 7\sqrt{234} - \sqrt{3718} + 2\sqrt{39}
\]
So, the final result is:
\[
7\sqrt{5577} - 7\sqrt{234} - \sqrt{3718} + 2\sqrt{39}
\]
This is the simplified form of the original expression.