Algebra Examples

${(7 m - 3)}^{2}$

Step 1

Simplify the expression.

Tap for more steps...

Step 1.1

Rewrite ${(7 m - 3)}^{2}$ as $(7 m - 3) (7 m - 3)$ .

$(7 m - 3) (7 m - 3)$

Step 1.2

Expand $(7 m - 3) (7 m - 3)$ using the FOIL Method.

Tap for more steps...

Step 1.2.1

Apply the distributive property.

$7 m (7 m - 3) - 3 (7 m - 3)$

Step 1.2.2

Apply the distributive property.

$7 m (7 m) + 7 m \cdot - 3 - 3 (7 m - 3)$

Step 1.2.3

Apply the distributive property.

$7 m (7 m) + 7 m \cdot - 3 - 3 (7 m) - 3 \cdot - 3$

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.

$7 \cdot 7 m \cdot m + 7 m \cdot - 3 - 3 (7 m) - 3 \cdot - 3$

Step 1.3.1.2

Multiply $m$ by $m$ by adding the exponents.

Tap for more steps...

Step 1.3.1.2.1

Move $m$ .

$7 \cdot 7 (m \cdot m) + 7 m \cdot - 3 - 3 (7 m) - 3 \cdot - 3$

Step 1.3.1.2.2

Multiply $m$ by $m$ .

$7 \cdot 7 m^{2} + 7 m \cdot - 3 - 3 (7 m) - 3 \cdot - 3$

Step 1.3.1.3

Multiply $7$ by $7$ .

$49 m^{2} + 7 m \cdot - 3 - 3 (7 m) - 3 \cdot - 3$

Step 1.3.1.4

Multiply $- 3$ by $7$ .

$49 m^{2} - 21 m - 3 (7 m) - 3 \cdot - 3$

Step 1.3.1.5

Multiply $7$ by $- 3$ .

$49 m^{2} - 21 m - 21 m - 3 \cdot - 3$

Step 1.3.1.6

Multiply $- 3$ by $- 3$ .

$49 m^{2} - 21 m - 21 m + 9$

Step 1.3.2

Subtract $21 m$ from $- 21 m$ .

$49 m^{2} - 42 m + 9$

Step 2

Use the form $a x^{2} + b x + c$ , to find the values of $a$ , $b$ , and $c$ .

$a = 49$

$b = - 42$

$c = 9$

Step 3

Consider the vertex form of a parabola.

$a {(x + d)}^{2} + e$

Step 4

Find the value of $d$ using the formula $d = \frac{b}{2 a}$ .

Tap for more steps...

Step 4.1

Substitute the values of $a$ and $b$ into the formula $d = \frac{b}{2 a}$ .

$d = \frac{- 42}{2 \cdot 49}$

Step 4.2

Simplify the right side.

Tap for more steps...

Step 4.2.1

Cancel the common factor of $- 42$ and $2$ .

Tap for more steps...

Step 4.2.1.1

Factor $2$ out of $- 42$ .

$d = \frac{2 \cdot - 21}{2 \cdot 49}$

Step 4.2.1.2

Cancel the common factors.

Tap for more steps...

Step 4.2.1.2.1

Factor $2$ out of $2 \cdot 49$ .

$d = \frac{2 \cdot - 21}{2 (49)}$

Step 4.2.1.2.2

Cancel the common factor.

$d = \frac{2 \cdot - 21}{2 \cdot 49}$

Step 4.2.1.2.3

Rewrite the expression.

$d = \frac{- 21}{49}$

Step 4.2.2

Cancel the common factor of $- 21$ and $49$ .

Tap for more steps...

Step 4.2.2.1

Factor $7$ out of $- 21$ .

$d = \frac{7 (- 3)}{49}$

Step 4.2.2.2

Cancel the common factors.

Tap for more steps...

Step 4.2.2.2.1

Factor $7$ out of $49$ .

$d = \frac{7 \cdot - 3}{7 \cdot 7}$

Step 4.2.2.2.2

Cancel the common factor.

$d = \frac{7 \cdot - 3}{7 \cdot 7}$

Step 4.2.2.2.3

Rewrite the expression.

$d = \frac{- 3}{7}$

Step 4.2.3

Move the negative in front of the fraction.

$d = - \frac{3}{7}$

Step 5

Find the value of $e$ using the formula $e = c - \frac{b^{2}}{4 a}$ .

Tap for more steps...

Step 5.1

Substitute the values of $c$ , $b$ and $a$ into the formula $e = c - \frac{b^{2}}{4 a}$ .

$e = 9 - \frac{{(- 42)}^{2}}{4 \cdot 49}$

Step 5.2

Simplify the right side.

Tap for more steps...

Step 5.2.1

Simplify each term.

Tap for more steps...

Step 5.2.1.1

Raise $- 42$ to the power of $2$ .

$e = 9 - \frac{1764}{4 \cdot 49}$

Step 5.2.1.2

Multiply $4$ by $49$ .

$e = 9 - \frac{1764}{196}$

Step 5.2.1.3

Divide $1764$ by $196$ .

$e = 9 - 1 \cdot 9$

Step 5.2.1.4

Multiply $- 1$ by $9$ .

$e = 9 - 9$

Step 5.2.2

Subtract $9$ from $9$ .

$e = 0$

Step 6

Substitute the values of $a$ , $d$ , and $e$ into the vertex form $49 {(m - \frac{3}{7})}^{2} + 0$ .

$49 {(m - \frac{3}{7})}^{2} + 0$