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Chapter 5: Q10. (page 231)

Simplify $2 p^{2} q (5 p q 鈭� 3 p^{3} q^{2} + 4 p q^{4})$ .

Short Answer

Expert verified

The simplified value of expression is $10 p^{3} q^{2} 鈭� 6 p^{5} q^{3} + 8 p^{3} q^{5}$ .

Step by step solution

01

Step 1. Write down the given expression.

The given expression to simplify is $2 p^{2} q (5 p q 鈭� 3 p^{3} q^{2} + 4 p q^{4})$ .

02

Step 2. Simplify the given expression.

Simplifying $2 p^{2} q (5 p q 鈭� 3 p^{3} q^{2} + 4 p q^{4})$ gives,

$\begin{matrix} 2 p^{2} q (5 p q 鈭� 3 p^{3} q^{2} + 4 p q^{4}) = (2 p^{2} q) (5 p q) 鈭� (2 p^{2} q) (3 p^{3} q^{2}) + (2 p^{2} q) (4 p q^{4}) \\ = 10 p^{2 + 1} q^{1 + 1} 鈭� 6 p^{2 + 3} q^{1 + 2} + 8 p^{2 + 1} q^{1 + 4} \\ = 10 p^{3} q^{2} 鈭� 6 p^{5} q^{3} + 8 p^{3} q^{5} \end{matrix}$

03

Step 3. Conclusion.

The simplified value of expression is $10 p^{3} q^{2} 鈭� 6 p^{5} q^{3} + 8 p^{3} q^{5}$

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