Expand the brackets for the following algebraic expression: $$ 6 x^{7} y^{2}\left(3 x^{4} y+5 x y^{6}\right) $$

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Let us expand the expression step by step.

1. We start with the expression:
   $$
   6x^{7}y^{2}\left(3x^{4}y + 5xy^{6}\right)
   $$

2. Distribute $$6x^{7}y^{2}$$ to each term inside the parentheses:
   $$
   6x^{7}y^{2} \cdot 3x^{4}y + 6x^{7}y^{2} \cdot 5xy^{6}
   $$

3. Multiply the coefficients:
   - For the first term: $$6 \cdot 3 = 18$$
   - For the second term: $$6 \cdot 5 = 30$$

4. Multiply the variables by adding the exponents:
   - For $$x$$:
     - First term: $$x^{7} \cdot x^{4} = x^{7+4} = x^{11}$$
     - Second term: $$x^{7} \cdot x = x^{7+1} = x^{8}$$
   - For $$y$$:
     - First term: $$y^{2} \cdot y = y^{2+1} = y^{3}$$
     - Second term: $$y^{2} \cdot y^{6} = y^{2+6} = y^{8}$$

5. Write the final expanded form:
   $$
   18x^{11}y^{3} + 30x^{8}y^{8}
   $$
The expanded form of the expression is $$18x^{11}y^{3} + 30x^{8}y^{8}$$.

Expand the brackets for the following algebraic expression: \[ 6 x^{7} y^{2}\left(3 x^{4} y+5 x y^{6}\right) \]

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