Algebra Examples

$- 3 y [\begin{array}{c} - 2 x & - y \\ - 4 y & - 3 x \end{array}]$

Step 1

Multiply $- 3 y$ by each element of the matrix.

$[\begin{array}{c} - 3 y (- 2 x) & - 3 y (- y) \\ - 3 y (- 4 y) & - 3 y (- 3 x) \end{array}]$

Step 2

Simplify each element in the matrix.

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Step 2.1

Rewrite using the commutative property of multiplication.

$[\begin{array}{c} - 3 \cdot - 2 y x & - 3 y (- y) \\ - 3 y (- 4 y) & - 3 y (- 3 x) \end{array}]$

Step 2.2

Multiply $- 3$ by $- 2$ .

$[\begin{array}{c} 6 y x & - 3 y (- y) \\ - 3 y (- 4 y) & - 3 y (- 3 x) \end{array}]$

Step 2.3

Rewrite using the commutative property of multiplication.

$[\begin{array}{c} 6 y x & - 3 \cdot - 1 y \cdot y \\ - 3 y (- 4 y) & - 3 y (- 3 x) \end{array}]$

Step 2.4

Multiply $y$ by $y$ by adding the exponents.

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Step 2.4.1

Move $y$ .

$[\begin{array}{c} 6 y x & - 3 \cdot - 1 (y \cdot y) \\ - 3 y (- 4 y) & - 3 y (- 3 x) \end{array}]$

Step 2.4.2

Multiply $y$ by $y$ .

$[\begin{array}{c} 6 y x & - 3 \cdot - 1 y^{2} \\ - 3 y (- 4 y) & - 3 y (- 3 x) \end{array}]$

Step 2.5

Multiply $- 3$ by $- 1$ .

$[\begin{array}{c} 6 y x & 3 y^{2} \\ - 3 y (- 4 y) & - 3 y (- 3 x) \end{array}]$

Step 2.6

Rewrite using the commutative property of multiplication.

$[\begin{array}{c} 6 y x & 3 y^{2} \\ - 3 \cdot - 4 y \cdot y & - 3 y (- 3 x) \end{array}]$

Step 2.7

Multiply $y$ by $y$ by adding the exponents.

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Step 2.7.1

Move $y$ .

$[\begin{array}{c} 6 y x & 3 y^{2} \\ - 3 \cdot - 4 (y \cdot y) & - 3 y (- 3 x) \end{array}]$

Step 2.7.2

Multiply $y$ by $y$ .

$[\begin{array}{c} 6 y x & 3 y^{2} \\ - 3 \cdot - 4 y^{2} & - 3 y (- 3 x) \end{array}]$

Step 2.8

Multiply $- 3$ by $- 4$ .

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

Step 2.9

Rewrite using the commutative property of multiplication.

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

Step 2.10

Multiply $- 3$ by $- 3$ .

$[\begin{array}{c} 6 y x & 3 y^{2} \\ 12 y^{2} & 9 y x \end{array}]$