Basic Math Examples

$(70 + 2 y) (50 + 2 y) = (70 \cdot 50) + 244$

Step 1

Simplify $(70 + 2 y) (50 + 2 y)$ .

Tap for more steps...

Step 1.1

Expand $(70 + 2 y) (50 + 2 y)$ using the FOIL Method.

Tap for more steps...

Step 1.1.1

Apply the distributive property.

$70 (50 + 2 y) + 2 y (50 + 2 y) = 70 \cdot 50 + 244$

Step 1.1.2

Apply the distributive property.

$70 \cdot 50 + 70 (2 y) + 2 y (50 + 2 y) = 70 \cdot 50 + 244$

Step 1.1.3

Apply the distributive property.

$70 \cdot 50 + 70 (2 y) + 2 y \cdot 50 + 2 y (2 y) = 70 \cdot 50 + 244$

Step 1.2

Simplify and combine like terms.

Tap for more steps...

Step 1.2.1

Simplify each term.

Tap for more steps...

Step 1.2.1.1

Multiply $70$ by $50$ .

$3500 + 70 (2 y) + 2 y \cdot 50 + 2 y (2 y) = 70 \cdot 50 + 244$

Step 1.2.1.2

Multiply $2$ by $70$ .

$3500 + 140 y + 2 y \cdot 50 + 2 y (2 y) = 70 \cdot 50 + 244$

Step 1.2.1.3

Multiply $50$ by $2$ .

$3500 + 140 y + 100 y + 2 y (2 y) = 70 \cdot 50 + 244$

Step 1.2.1.4

Rewrite using the commutative property of multiplication.

$3500 + 140 y + 100 y + 2 \cdot 2 y \cdot y = 70 \cdot 50 + 244$

Step 1.2.1.5

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

Tap for more steps...

Step 1.2.1.5.1

Move $y$ .

$3500 + 140 y + 100 y + 2 \cdot 2 (y \cdot y) = 70 \cdot 50 + 244$

Step 1.2.1.5.2

Multiply $y$ by $y$ .

$3500 + 140 y + 100 y + 2 \cdot 2 y^{2} = 70 \cdot 50 + 244$

Step 1.2.1.6

Multiply $2$ by $2$ .

$3500 + 140 y + 100 y + 4 y^{2} = 70 \cdot 50 + 244$

Step 1.2.2

Add $140 y$ and $100 y$ .

$3500 + 240 y + 4 y^{2} = 70 \cdot 50 + 244$

Step 2

Simplify $70 \cdot 50 + 244$ .

Tap for more steps...

Step 2.1

Multiply $70$ by $50$ .

$3500 + 240 y + 4 y^{2} = 3500 + 244$

Step 2.2

Add $3500$ and $244$ .

$3500 + 240 y + 4 y^{2} = 3744$

Step 3

Subtract $3744$ from both sides of the equation.

$3500 + 240 y + 4 y^{2} - 3744 = 0$

Step 4

Subtract $3744$ from $3500$ .

$240 y + 4 y^{2} - 244 = 0$

Step 5

Factor the left side of the equation.

Tap for more steps...

Step 5.1

Factor $4$ out of $240 y + 4 y^{2} - 244$ .

Tap for more steps...

Step 5.1.1

Factor $4$ out of $240 y$ .

$4 (60 y) + 4 y^{2} - 244 = 0$

Step 5.1.2

Factor $4$ out of $4 y^{2}$ .

$4 (60 y) + 4 (y^{2}) - 244 = 0$

Step 5.1.3

Factor $4$ out of $- 244$ .

$4 (60 y) + 4 y^{2} + 4 \cdot - 61 = 0$

Step 5.1.4

Factor $4$ out of $4 (60 y) + 4 y^{2}$ .

$4 (60 y + y^{2}) + 4 \cdot - 61 = 0$

Step 5.1.5

Factor $4$ out of $4 (60 y + y^{2}) + 4 \cdot - 61$ .

$4 (60 y + y^{2} - 61) = 0$

Step 5.2

Let $u = y$ . Substitute $u$ for all occurrences of $y$ .

$4 (60 u + u^{2} - 61) = 0$

Step 5.3

Factor $60 u + u^{2} - 61$ using the AC method.

Tap for more steps...

Step 5.3.1

Consider the form $x^{2} + b x + c$ . Find a pair of integers whose product is $c$ and whose sum is $b$ . In this case, whose product is $- 61$ and whose sum is $60$ .

$- 1, 61$

Step 5.3.2

Write the factored form using these integers.

$4 ((u - 1) (u + 61)) = 0$

Step 5.4

Factor.

Tap for more steps...

Step 5.4.1

Replace all occurrences of $u$ with $y$ .

$4 ((y - 1) (y + 61)) = 0$

Step 5.4.2

Remove unnecessary parentheses.

$4 (y - 1) (y + 61) = 0$

Step 6

If any individual factor on the left side of the equation is equal to $0$ , the entire expression will be equal to $0$ .

$y - 1 = 0$

$y + 61 = 0$

Step 7

Set $y - 1$ equal to $0$ and solve for $y$ .

Tap for more steps...

Step 7.1

Set $y - 1$ equal to $0$ .

$y - 1 = 0$

Step 7.2

Add $1$ to both sides of the equation.

$y = 1$

Step 8

Set $y + 61$ equal to $0$ and solve for $y$ .

Tap for more steps...

Step 8.1

Set $y + 61$ equal to $0$ .

$y + 61 = 0$

Step 8.2

Subtract $61$ from both sides of the equation.

$y = - 61$

Step 9

The final solution is all the values that make $4 (y - 1) (y + 61) = 0$ true.

$y = 1, - 61$