Basic Math Examples

${(5 y - 2)}^{2} + 3 (5 y - 2) + 9$

Step 1

Simplify each term.

Tap for more steps...

Step 1.1

Rewrite ${(5 y - 2)}^{2}$ as $(5 y - 2) (5 y - 2)$ .

$(5 y - 2) (5 y - 2) + 3 (5 y - 2) + 9$

Step 1.2

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

Tap for more steps...

Step 1.2.1

Apply the distributive property.

$5 y (5 y - 2) - 2 (5 y - 2) + 3 (5 y - 2) + 9$

Step 1.2.2

Apply the distributive property.

$5 y (5 y) + 5 y \cdot - 2 - 2 (5 y - 2) + 3 (5 y - 2) + 9$

Step 1.2.3

Apply the distributive property.

$5 y (5 y) + 5 y \cdot - 2 - 2 (5 y) - 2 \cdot - 2 + 3 (5 y - 2) + 9$

Step 1.3

Simplify and combine like terms.

Tap for more steps...

Step 1.3.1

Simplify each term.

Tap for more steps...

Step 1.3.1.1

Rewrite using the commutative property of multiplication.

$5 \cdot 5 y \cdot y + 5 y \cdot - 2 - 2 (5 y) - 2 \cdot - 2 + 3 (5 y - 2) + 9$

Step 1.3.1.2

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

Tap for more steps...

Step 1.3.1.2.1

Move $y$ .

$5 \cdot 5 (y \cdot y) + 5 y \cdot - 2 - 2 (5 y) - 2 \cdot - 2 + 3 (5 y - 2) + 9$

Step 1.3.1.2.2

Multiply $y$ by $y$ .

$5 \cdot 5 y^{2} + 5 y \cdot - 2 - 2 (5 y) - 2 \cdot - 2 + 3 (5 y - 2) + 9$

Step 1.3.1.3

Multiply $5$ by $5$ .

$25 y^{2} + 5 y \cdot - 2 - 2 (5 y) - 2 \cdot - 2 + 3 (5 y - 2) + 9$

Step 1.3.1.4

Multiply $- 2$ by $5$ .

$25 y^{2} - 10 y - 2 (5 y) - 2 \cdot - 2 + 3 (5 y - 2) + 9$

Step 1.3.1.5

Multiply $5$ by $- 2$ .

$25 y^{2} - 10 y - 10 y - 2 \cdot - 2 + 3 (5 y - 2) + 9$

Step 1.3.1.6

Multiply $- 2$ by $- 2$ .

$25 y^{2} - 10 y - 10 y + 4 + 3 (5 y - 2) + 9$

Step 1.3.2

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

$25 y^{2} - 20 y + 4 + 3 (5 y - 2) + 9$

Step 1.4

Apply the distributive property.

$25 y^{2} - 20 y + 4 + 3 (5 y) + 3 \cdot - 2 + 9$

Step 1.5

Multiply $5$ by $3$ .

$25 y^{2} - 20 y + 4 + 15 y + 3 \cdot - 2 + 9$

Step 1.6

Multiply $3$ by $- 2$ .

$25 y^{2} - 20 y + 4 + 15 y - 6 + 9$

Step 2

Simplify by adding terms.

Tap for more steps...

Step 2.1

Add $- 20 y$ and $15 y$ .

$25 y^{2} - 5 y + 4 - 6 + 9$

Step 2.2

Simplify by adding and subtracting.

Tap for more steps...

Step 2.2.1

Subtract $6$ from $4$ .

$25 y^{2} - 5 y - 2 + 9$

Step 2.2.2

Add $- 2$ and $9$ .

$25 y^{2} - 5 y + 7$