Basic Math Examples

$(4 y + 5) (7 y^{2} - 3 y - 2)$

Step 1

Expand $(4 y + 5) (7 y^{2} - 3 y - 2)$ by multiplying each term in the first expression by each term in the second expression.

$4 y (7 y^{2}) + 4 y (- 3 y) + 4 y \cdot - 2 + 5 (7 y^{2}) + 5 (- 3 y) + 5 \cdot - 2$

Step 2

Simplify terms.

Tap for more steps...

Step 2.1

Simplify each term.

Tap for more steps...

Step 2.1.1

Rewrite using the commutative property of multiplication.

$4 \cdot 7 y \cdot y^{2} + 4 y (- 3 y) + 4 y \cdot - 2 + 5 (7 y^{2}) + 5 (- 3 y) + 5 \cdot - 2$

Step 2.1.2

Multiply $y$ by $y^{2}$ by adding the exponents.

Tap for more steps...

Step 2.1.2.1

Move $y^{2}$ .

$4 \cdot 7 (y^{2} y) + 4 y (- 3 y) + 4 y \cdot - 2 + 5 (7 y^{2}) + 5 (- 3 y) + 5 \cdot - 2$

Step 2.1.2.2

Multiply $y^{2}$ by $y$ .

Tap for more steps...

Step 2.1.2.2.1

Raise $y$ to the power of $1$ .

$4 \cdot 7 (y^{2} y^{1}) + 4 y (- 3 y) + 4 y \cdot - 2 + 5 (7 y^{2}) + 5 (- 3 y) + 5 \cdot - 2$

Step 2.1.2.2.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$4 \cdot 7 y^{2 + 1} + 4 y (- 3 y) + 4 y \cdot - 2 + 5 (7 y^{2}) + 5 (- 3 y) + 5 \cdot - 2$

Step 2.1.2.3

Add $2$ and $1$ .

$4 \cdot 7 y^{3} + 4 y (- 3 y) + 4 y \cdot - 2 + 5 (7 y^{2}) + 5 (- 3 y) + 5 \cdot - 2$

Step 2.1.3

Multiply $4$ by $7$ .

$28 y^{3} + 4 y (- 3 y) + 4 y \cdot - 2 + 5 (7 y^{2}) + 5 (- 3 y) + 5 \cdot - 2$

Step 2.1.4

Rewrite using the commutative property of multiplication.

$28 y^{3} + 4 \cdot - 3 y \cdot y + 4 y \cdot - 2 + 5 (7 y^{2}) + 5 (- 3 y) + 5 \cdot - 2$

Step 2.1.5

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

Tap for more steps...

Step 2.1.5.1

Move $y$ .

$28 y^{3} + 4 \cdot - 3 (y \cdot y) + 4 y \cdot - 2 + 5 (7 y^{2}) + 5 (- 3 y) + 5 \cdot - 2$

Step 2.1.5.2

Multiply $y$ by $y$ .

$28 y^{3} + 4 \cdot - 3 y^{2} + 4 y \cdot - 2 + 5 (7 y^{2}) + 5 (- 3 y) + 5 \cdot - 2$

Step 2.1.6

Multiply $4$ by $- 3$ .

$28 y^{3} - 12 y^{2} + 4 y \cdot - 2 + 5 (7 y^{2}) + 5 (- 3 y) + 5 \cdot - 2$

Step 2.1.7

Multiply $- 2$ by $4$ .

$28 y^{3} - 12 y^{2} - 8 y + 5 (7 y^{2}) + 5 (- 3 y) + 5 \cdot - 2$

Step 2.1.8

Multiply $7$ by $5$ .

$28 y^{3} - 12 y^{2} - 8 y + 35 y^{2} + 5 (- 3 y) + 5 \cdot - 2$

Step 2.1.9

Multiply $- 3$ by $5$ .

$28 y^{3} - 12 y^{2} - 8 y + 35 y^{2} - 15 y + 5 \cdot - 2$

Step 2.1.10

Multiply $5$ by $- 2$ .

$28 y^{3} - 12 y^{2} - 8 y + 35 y^{2} - 15 y - 10$

Step 2.2

Simplify by adding terms.

Tap for more steps...

Step 2.2.1

Add $- 12 y^{2}$ and $35 y^{2}$ .

$28 y^{3} + 23 y^{2} - 8 y - 15 y - 10$

Step 2.2.2

Subtract $15 y$ from $- 8 y$ .

$28 y^{3} + 23 y^{2} - 23 y - 10$