Simplify the Matrix [[6y,y^2],[-2y,-2y]]*[[-y,xy],[-6,x^2]]-[[6y,-6],[-3y,y]]

$[\begin{array}{c} 6 y & y^{2} \\ - 2 y & - 2 y \end{array}] \cdot [\begin{array}{c} - y & x y \\ - 6 & x^{2} \end{array}] - [\begin{array}{c} 6 y & - 6 \\ - 3 y & y \end{array}]$

Multiply each row in the first matrix by each column in the second matrix.

$[\begin{array}{c} 6 y \cdot (- y) + y^{2} \cdot - 6 & 6 y \cdot (x y) + y^{2} \cdot x^{2} \\ - 2 y \cdot (- y) - 2 y \cdot - 6 & - 2 y \cdot (x y) - 2 y \cdot x^{2} \end{array}] - [\begin{array}{c} 6 y & - 6 \\ - 3 y & y \end{array}]$

Simplify each element of the matrix by multiplying out all the expressions.

$[\begin{array}{c} - 12 y^{2} & 6 y^{2} x + y^{2} x^{2} \\ 2 y^{2} + 12 y & - 2 y^{2} x - 2 y x^{2} \end{array}] - [\begin{array}{c} 6 y & - 6 \\ - 3 y & y \end{array}]$

Simplify each element in the matrix.

Rearrange $6 y^{2} x + y^{2} x^{2}$ .

$[\begin{array}{c} - 12 y^{2} & x^{2} y^{2} + 6 x y^{2} \\ 2 y^{2} + 12 y & - 2 y^{2} x - 2 y x^{2} \end{array}] - [\begin{array}{c} 6 y & - 6 \\ - 3 y & y \end{array}]$

Rearrange $- 2 y^{2} x - 2 y x^{2}$ .

$[\begin{array}{c} - 12 y^{2} & x^{2} y^{2} + 6 x y^{2} \\ 2 y^{2} + 12 y & - 2 x^{2} y - 2 x y^{2} \end{array}] - [\begin{array}{c} 6 y & - 6 \\ - 3 y & y \end{array}]$

Subtract the corresponding elements.

$[\begin{array}{c} - 12 y^{2} - 6 y & x^{2} y^{2} + 6 x y^{2} - (- 6) \\ 2 y^{2} + 12 y - (- 3 y) & - 2 x^{2} y - 2 x y^{2} - y \end{array}]$

Simplify each element of the matrix $[\begin{array}{c} - 12 y^{2} - 6 y & x^{2} y^{2} + 6 x y^{2} - (- 6) \\ 2 y^{2} + 12 y - (- 3 y) & - 2 x^{2} y - 2 x y^{2} - y \end{array}]$ .

Simplify $x^{2} y^{2} + 6 x y^{2} - (- 6)$ .

$[\begin{array}{c} - 12 y^{2} - 6 y & x^{2} y^{2} + 6 x y^{2} + 6 \\ 2 y^{2} + 12 y - (- 3 y) & - 2 x^{2} y - 2 x y^{2} - y \end{array}]$

Simplify $2 y^{2} + 12 y - (- 3 y)$ .

$[\begin{array}{c} - 12 y^{2} - 6 y & x^{2} y^{2} + 6 x y^{2} + 6 \\ 2 y^{2} + 15 y & - 2 x^{2} y - 2 x y^{2} - y \end{array}]$

Simplify the Matrix [[6y,y^2],[-2y,-2y]]*[[-y,xy],[-6,x^2]]-[[6y,-6],[-3y,y]]

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