Expand the Trigonometric Expression (t+1)^2

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

Step 1

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

$(t + 1) (t + 1)$

Step 2

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

Apply the distributive property.

$t (t + 1) + 1 (t + 1)$

Apply the distributive property.

$t \cdot t + t \cdot 1 + 1 (t + 1)$

Apply the distributive property.

$t \cdot t + t \cdot 1 + 1 t + 1 \cdot 1$

$t \cdot t + t \cdot 1 + 1 t + 1 \cdot 1$

Step 3

Simplify and combine like terms.

Simplify each term.

Multiply $t$ by $t$ .

$t^{2} + t \cdot 1 + 1 t + 1 \cdot 1$

Multiply $t$ by $1$ .

$t^{2} + t + 1 t + 1 \cdot 1$

Multiply $t$ by $1$ .

$t^{2} + t + t + 1 \cdot 1$

Multiply $1$ by $1$ .

$t^{2} + t + t + 1$

$t^{2} + t + t + 1$

Add $t$ and $t$ .

$t^{2} + 2 t + 1$

$t^{2} + 2 t + 1$

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