Patel Schofield
10/21/2023 · Primary School
1 lallev \( 1\left(x^{a+5}-3 x^{a+4}+x^{a+3}-5 x^{a+1}\right)\left(-2 x^{2}\right) \) \( =\left(\frac{2}{9} x^{4}-x^{2} y^{2}+\frac{1}{3} y^{4}\right)\left(\frac{3}{7} x^{3} y^{4}\right) \) \( 3\left(a^{4} b^{4}+a^{m-1} b^{n+1}-a^{m-2} b^{n+2}\right)\left(3 a^{2} b\right) \) \( 4\left(\frac{1}{3} x^{2}-\frac{2}{5} x y-\frac{1}{4} y^{2}\right)\left(\frac{3}{2} y^{2}\right) \) \( \left(-\frac{2}{11} a^{x-1} b^{x-3} c^{2}\right)\left(-\frac{44}{7} a^{x-3} b^{2}\right) \) \( \left(-\frac{1}{8} m^{3} n^{4}\right)\left(-\frac{4}{5} a^{3} m^{2} n\right) \) \( \left(a^{4}-6 a^{3} x+9 a^{2} x^{2}-8\right)\left(3 b x^{3}\right) \)
UpStudy ThothAI Solution
Tutor-Verified Answer
Step-by-step Solution
Let's simplify each expression step by step.
1. **First Expression:**
\[
1\left(x^{a+5}-3 x^{a+4}+x^{a+3}-5 x^{a+1}\right)\left(-2 x^{2}\right)
\]
Distributing \(-2x^2\):
\[
-2x^2\left(x^{a+5}-3 x^{a+4}+x^{a+3}-5 x^{a+1}\right) = -2\left(x^{a+7} - 3x^{a+6} + x^{a+5} - 5x^{a+3}\right)
\]
2. **Second Expression:**
\[
\left(\frac{2}{9} x^{4}-x^{2} y^{2}+\frac{1}{3} y^{4}\right)\left(\frac{3}{7} x^{3} y^{4}\right)
\]
Distributing \(\frac{3}{7} x^{3} y^{4}\):
\[
= \frac{3}{7} x^{3} y^{4} \cdot \frac{2}{9} x^{4} + \frac{3}{7} x^{3} y^{4} \cdot (-x^{2} y^{2}) + \frac{3}{7} x^{3} y^{4} \cdot \frac{1}{3} y^{4}
\]
\[
= \frac{6}{63} x^{7} y^{4} - \frac{3}{7} x^{5} y^{6} + \frac{1}{7} x^{3} y^{8}
\]
\[
= \frac{2}{21} x^{7} y^{4} - \frac{3}{7} x^{5} y^{6} + \frac{1}{7} x^{3} y^{8}
\]
3. **Third Expression:**
\[
3\left(a^{4} b^{4}+a^{m-1} b^{n+1}-a^{m-2} b^{n+2}\right)\left(3 a^{2} b\right)
\]
Distributing \(3a^2b\):
\[
= 9a^{4} b^{5} + 9a^{m+1} b^{n+2} - 9a^{m} b^{n+3}
\]
4. **Fourth Expression:**
\[
4\left(\frac{1}{3} x^{2}-\frac{2}{5} x y-\frac{1}{4} y^{2}\right)\left(\frac{3}{2} y^{2}\right)
\]
Distributing \(\frac{3}{2}y^{2}\):
\[
= 4\left(\frac{1}{3} x^{2} \cdot \frac{3}{2} y^{2} - \frac{2}{5} x y \cdot \frac{3}{2} y^{2} - \frac{1}{4} y^{2} \cdot \frac{3}{2} y^{2}\right)
\]
\[
= 4\left(\frac{1}{2} x^{2} y^{2} - \frac{3}{5} x y^{3} - \frac{3}{8} y^{4}\right)
\]
\[
= 2 x^{2} y^{2} - \frac{12}{5} x y^{3} - \frac{3}{2} y^{4}
\]
5. **Fifth Expression:**
\[
\left(-\frac{2}{11} a^{x-1} b^{x-3} c^{2}\right)\left(-\frac{44}{7} a^{x-3} b^{2}\right)
\]
Multiplying:
\[
= \frac{88}{77} a^{(x-1)+(x-3)} b^{(x-3)+2} c^{2} = \frac{88}{77} a^{2x-4} b^{x-1} c^{2}
\]
6. **Sixth Expression:**
\[
\left(-\frac{1}{8} m^{3} n^{4}\right)\left(-\frac
Quick Answer
1. \(-2x^{a+7} + 3x^{a+6} - x^{a+5} + 5x^{a+3}\)
2. \(\frac{2}{21}x^{7}y^{4} - \frac{3}{7}x^{5}y^{6} + \frac{1}{7}x^{3}y^{8}\)
3. \(9a^{4}b^{5} + 9a^{m+1}b^{n+2} - 9a^{m}b^{n+3}\)
4. \(2x^{2}y^{2} - \frac{12}{5}xy^{3} - \frac{3}{2}y^{4}\)
5. \(\frac{88}{77}a^{2x-4}b^{x-1}c^{2}\)
6. \(\frac{1}{8}m^{3}n^{4} \cdot \frac{4}{5}a^{3}m^{2}n = \frac{1}{10}a^{5}m^{5}n^{5}\)
7. \(3a^{4}b^{5}x^{3} - 18a^{3}bx^{3} + 27a^{2}b^{2}x^{3} - 24bx^{3} + 24b^{2}x^{3}\)
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