Basic Math Examples

$(4 y - 6) (2 y + 5 u - 7)$

Step 1

Expand $(4 y - 6) (2 y + 5 u - 7)$ by multiplying each term in the first expression by each term in the second expression.

$4 y (2 y) + 4 y (5 u) + 4 y \cdot - 7 - 6 (2 y) - 6 (5 u) - 6 \cdot - 7$

Step 2

Simplify terms.

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Step 2.1

Simplify each term.

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Step 2.1.1

Rewrite using the commutative property of multiplication.

$4 \cdot 2 y \cdot y + 4 y (5 u) + 4 y \cdot - 7 - 6 (2 y) - 6 (5 u) - 6 \cdot - 7$

Step 2.1.2

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

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Step 2.1.2.1

Move $y$ .

$4 \cdot 2 (y \cdot y) + 4 y (5 u) + 4 y \cdot - 7 - 6 (2 y) - 6 (5 u) - 6 \cdot - 7$

Step 2.1.2.2

Multiply $y$ by $y$ .

$4 \cdot 2 y^{2} + 4 y (5 u) + 4 y \cdot - 7 - 6 (2 y) - 6 (5 u) - 6 \cdot - 7$

Step 2.1.3

Multiply $4$ by $2$ .

$8 y^{2} + 4 y (5 u) + 4 y \cdot - 7 - 6 (2 y) - 6 (5 u) - 6 \cdot - 7$

Step 2.1.4

Rewrite using the commutative property of multiplication.

$8 y^{2} + 4 \cdot 5 y u + 4 y \cdot - 7 - 6 (2 y) - 6 (5 u) - 6 \cdot - 7$

Step 2.1.5

Multiply $4$ by $5$ .

$8 y^{2} + 20 y u + 4 y \cdot - 7 - 6 (2 y) - 6 (5 u) - 6 \cdot - 7$

Step 2.1.6

Multiply $- 7$ by $4$ .

$8 y^{2} + 20 y u - 28 y - 6 (2 y) - 6 (5 u) - 6 \cdot - 7$

Step 2.1.7

Multiply $2$ by $- 6$ .

$8 y^{2} + 20 y u - 28 y - 12 y - 6 (5 u) - 6 \cdot - 7$

Step 2.1.8

Multiply $5$ by $- 6$ .

$8 y^{2} + 20 y u - 28 y - 12 y - 30 u - 6 \cdot - 7$

Step 2.1.9

Multiply $- 6$ by $- 7$ .

$8 y^{2} + 20 y u - 28 y - 12 y - 30 u + 42$

Step 2.2

Simplify by adding terms.

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Step 2.2.1

Subtract $12 y$ from $- 28 y$ .

$8 y^{2} + 20 y u - 40 y - 30 u + 42$

Step 2.2.2

Simplify the expression.

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Step 2.2.2.1

Move $y$ .

$8 y^{2} + 20 u y - 40 y - 30 u + 42$

Step 2.2.2.2

Move $- 40 y$ .

$8 y^{2} + 20 u y - 30 u - 40 y + 42$

Step 2.2.2.3

Reorder $8 y^{2}$ and $20 u y$ .

$20 u y + 8 y^{2} - 30 u - 40 y + 42$