Precalculus Examples

$(t - 1) (t - 4) = {(t + 1)}^{2}$

Step 1

Simplify $(t - 1) (t - 4)$ .

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Step 1.1

Rewrite.

$0 + 0 + (t - 1) (t - 4) = {(t + 1)}^{2}$

Step 1.2

Simplify by adding zeros.

$(t - 1) (t - 4) = {(t + 1)}^{2}$

Step 1.3

Expand $(t - 1) (t - 4)$ using the FOIL Method.

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Step 1.3.1

Apply the distributive property.

$t (t - 4) - 1 (t - 4) = {(t + 1)}^{2}$

Step 1.3.2

Apply the distributive property.

$t \cdot t + t \cdot - 4 - 1 (t - 4) = {(t + 1)}^{2}$

Step 1.3.3

Apply the distributive property.

$t \cdot t + t \cdot - 4 - 1 t - 1 \cdot - 4 = {(t + 1)}^{2}$

Step 1.4

Simplify and combine like terms.

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Step 1.4.1

Simplify each term.

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Step 1.4.1.1

Multiply $t$ by $t$ .

$t^{2} + t \cdot - 4 - 1 t - 1 \cdot - 4 = {(t + 1)}^{2}$

Step 1.4.1.2

Move $- 4$ to the left of $t$ .

$t^{2} - 4 \cdot t - 1 t - 1 \cdot - 4 = {(t + 1)}^{2}$

Step 1.4.1.3

Rewrite $- 1 t$ as $- t$ .

$t^{2} - 4 t - t - 1 \cdot - 4 = {(t + 1)}^{2}$

Step 1.4.1.4

Multiply $- 1$ by $- 4$ .

$t^{2} - 4 t - t + 4 = {(t + 1)}^{2}$

Step 1.4.2

Subtract $t$ from $- 4 t$ .

$t^{2} - 5 t + 4 = {(t + 1)}^{2}$

Step 2

Simplify ${(t + 1)}^{2}$ .

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Step 2.1

Rewrite ${(t + 1)}^{2}$ as $(t + 1) (t + 1)$ .

$t^{2} - 5 t + 4 = (t + 1) (t + 1)$

Step 2.2

Expand $(t + 1) (t + 1)$ using the FOIL Method.

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Step 2.2.1

Apply the distributive property.

$t^{2} - 5 t + 4 = t (t + 1) + 1 (t + 1)$

Step 2.2.2

Apply the distributive property.

$t^{2} - 5 t + 4 = t \cdot t + t \cdot 1 + 1 (t + 1)$

Step 2.2.3

Apply the distributive property.

$t^{2} - 5 t + 4 = t \cdot t + t \cdot 1 + 1 t + 1 \cdot 1$

Step 2.3

Simplify and combine like terms.

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Step 2.3.1

Simplify each term.

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Step 2.3.1.1

Multiply $t$ by $t$ .

$t^{2} - 5 t + 4 = t^{2} + t \cdot 1 + 1 t + 1 \cdot 1$

Step 2.3.1.2

Multiply $t$ by $1$ .

$t^{2} - 5 t + 4 = t^{2} + t + 1 t + 1 \cdot 1$

Step 2.3.1.3

Multiply $t$ by $1$ .

$t^{2} - 5 t + 4 = t^{2} + t + t + 1 \cdot 1$

Step 2.3.1.4

Multiply $1$ by $1$ .

$t^{2} - 5 t + 4 = t^{2} + t + t + 1$

Step 2.3.2

Add $t$ and $t$ .

$t^{2} - 5 t + 4 = t^{2} + 2 t + 1$

Step 3

Move all terms containing $t$ to the left side of the equation.

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Step 3.1

Subtract $t^{2}$ from both sides of the equation.

$t^{2} - 5 t + 4 - t^{2} = 2 t + 1$

Step 3.2

Subtract $2 t$ from both sides of the equation.

$t^{2} - 5 t + 4 - t^{2} - 2 t = 1$

Step 3.3

Combine the opposite terms in $t^{2} - 5 t + 4 - t^{2} - 2 t$ .

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Step 3.3.1

Subtract $t^{2}$ from $t^{2}$ .

$- 5 t + 4 + 0 - 2 t = 1$

Step 3.3.2

Add $- 5 t + 4$ and $0$ .

$- 5 t + 4 - 2 t = 1$

Step 3.4

Subtract $2 t$ from $- 5 t$ .

$- 7 t + 4 = 1$

Step 4

Move all terms not containing $t$ to the right side of the equation.

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Step 4.1

Subtract $4$ from both sides of the equation.

$- 7 t = 1 - 4$

Step 4.2

Subtract $4$ from $1$ .

$- 7 t = - 3$

Step 5

Divide each term in $- 7 t = - 3$ by $- 7$ and simplify.

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Step 5.1

Divide each term in $- 7 t = - 3$ by $- 7$ .

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

Step 5.2

Simplify the left side.

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Step 5.2.1

Cancel the common factor of $- 7$ .

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Step 5.2.1.1

Cancel the common factor.

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

Step 5.2.1.2

Divide $t$ by $1$ .

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

Step 5.3

Simplify the right side.

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Step 5.3.1

Dividing two negative values results in a positive value.

$t = \frac{3}{7}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$t = \frac{3}{7}$

Decimal Form:

$t = 0.\overline{428571}$