Algebra Examples

$(3 y - 5) (2 y - 7) (4 y + 1)$

Step 1

Expand $(3 y - 5) (2 y - 7)$ using the FOIL Method.

Tap for more steps...

Step 1.1

Apply the distributive property.

$(3 y (2 y - 7) - 5 (2 y - 7)) (4 y + 1)$

Step 1.2

Apply the distributive property.

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

Step 1.3

Apply the distributive property.

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

Step 2

Simplify and combine like 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.

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

Step 2.1.2

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

Tap for more steps...

Step 2.1.2.1

Move $y$ .

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

Step 2.1.2.2

Multiply $y$ by $y$ .

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

Step 2.1.3

Multiply $3$ by $2$ .

$(6 y^{2} + 3 y \cdot - 7 - 5 (2 y) - 5 \cdot - 7) (4 y + 1)$

Step 2.1.4

Multiply $- 7$ by $3$ .

$(6 y^{2} - 21 y - 5 (2 y) - 5 \cdot - 7) (4 y + 1)$

Step 2.1.5

Multiply $2$ by $- 5$ .

$(6 y^{2} - 21 y - 10 y - 5 \cdot - 7) (4 y + 1)$

Step 2.1.6

Multiply $- 5$ by $- 7$ .

$(6 y^{2} - 21 y - 10 y + 35) (4 y + 1)$

Step 2.2

Subtract $10 y$ from $- 21 y$ .

$(6 y^{2} - 31 y + 35) (4 y + 1)$

Step 3

Expand $(6 y^{2} - 31 y + 35) (4 y + 1)$ by multiplying each term in the first expression by each term in the second expression.

$6 y^{2} (4 y) + 6 y^{2} \cdot 1 - 31 y (4 y) - 31 y \cdot 1 + 35 (4 y) + 35 \cdot 1$

Step 4

Simplify terms.

Tap for more steps...

Step 4.1

Simplify each term.

Tap for more steps...

Step 4.1.1

Rewrite using the commutative property of multiplication.

$6 \cdot 4 y^{2} y + 6 y^{2} \cdot 1 - 31 y (4 y) - 31 y \cdot 1 + 35 (4 y) + 35 \cdot 1$

Step 4.1.2

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

Tap for more steps...

Step 4.1.2.1

Move $y$ .

$6 \cdot 4 (y \cdot y^{2}) + 6 y^{2} \cdot 1 - 31 y (4 y) - 31 y \cdot 1 + 35 (4 y) + 35 \cdot 1$

Step 4.1.2.2

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

Tap for more steps...

Step 4.1.2.2.1

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

$6 \cdot 4 (y^{1} y^{2}) + 6 y^{2} \cdot 1 - 31 y (4 y) - 31 y \cdot 1 + 35 (4 y) + 35 \cdot 1$

Step 4.1.2.2.2

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

$6 \cdot 4 y^{1 + 2} + 6 y^{2} \cdot 1 - 31 y (4 y) - 31 y \cdot 1 + 35 (4 y) + 35 \cdot 1$

Step 4.1.2.3

Add $1$ and $2$ .

$6 \cdot 4 y^{3} + 6 y^{2} \cdot 1 - 31 y (4 y) - 31 y \cdot 1 + 35 (4 y) + 35 \cdot 1$

Step 4.1.3

Multiply $6$ by $4$ .

$24 y^{3} + 6 y^{2} \cdot 1 - 31 y (4 y) - 31 y \cdot 1 + 35 (4 y) + 35 \cdot 1$

Step 4.1.4

Multiply $6$ by $1$ .

$24 y^{3} + 6 y^{2} - 31 y (4 y) - 31 y \cdot 1 + 35 (4 y) + 35 \cdot 1$

Step 4.1.5

Rewrite using the commutative property of multiplication.

$24 y^{3} + 6 y^{2} - 31 \cdot 4 y \cdot y - 31 y \cdot 1 + 35 (4 y) + 35 \cdot 1$

Step 4.1.6

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

Tap for more steps...

Step 4.1.6.1

Move $y$ .

$24 y^{3} + 6 y^{2} - 31 \cdot 4 (y \cdot y) - 31 y \cdot 1 + 35 (4 y) + 35 \cdot 1$

Step 4.1.6.2

Multiply $y$ by $y$ .

$24 y^{3} + 6 y^{2} - 31 \cdot 4 y^{2} - 31 y \cdot 1 + 35 (4 y) + 35 \cdot 1$

Step 4.1.7

Multiply $- 31$ by $4$ .

$24 y^{3} + 6 y^{2} - 124 y^{2} - 31 y \cdot 1 + 35 (4 y) + 35 \cdot 1$

Step 4.1.8

Multiply $- 31$ by $1$ .

$24 y^{3} + 6 y^{2} - 124 y^{2} - 31 y + 35 (4 y) + 35 \cdot 1$

Step 4.1.9

Multiply $4$ by $35$ .

$24 y^{3} + 6 y^{2} - 124 y^{2} - 31 y + 140 y + 35 \cdot 1$

Step 4.1.10

Multiply $35$ by $1$ .

$24 y^{3} + 6 y^{2} - 124 y^{2} - 31 y + 140 y + 35$

Step 4.2

Simplify by adding terms.

Tap for more steps...

Step 4.2.1

Subtract $124 y^{2}$ from $6 y^{2}$ .

$24 y^{3} - 118 y^{2} - 31 y + 140 y + 35$

Step 4.2.2

Add $- 31 y$ and $140 y$ .

$24 y^{3} - 118 y^{2} + 109 y + 35$