Algebra Examples

${(10 + 2 t)}^{2}$

Step 1

To write a polynomial in standard form, simplify and then arrange the terms in descending order.

$a x^{2} + b x + c$

Step 2

Rewrite ${(10 + 2 t)}^{2}$ as $(10 + 2 t) (10 + 2 t)$ .

$(10 + 2 t) (10 + 2 t)$

Step 3

Expand $(10 + 2 t) (10 + 2 t)$ using the FOIL Method.

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Step 3.1

Apply the distributive property.

$10 (10 + 2 t) + 2 t (10 + 2 t)$

Step 3.2

Apply the distributive property.

$10 \cdot 10 + 10 (2 t) + 2 t (10 + 2 t)$

Step 3.3

Apply the distributive property.

$10 \cdot 10 + 10 (2 t) + 2 t \cdot 10 + 2 t (2 t)$

Step 4

Simplify and combine like terms.

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Step 4.1

Simplify each term.

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Step 4.1.1

Multiply $10$ by $10$ .

$100 + 10 (2 t) + 2 t \cdot 10 + 2 t (2 t)$

Step 4.1.2

Multiply $2$ by $10$ .

$100 + 20 t + 2 t \cdot 10 + 2 t (2 t)$

Step 4.1.3

Multiply $10$ by $2$ .

$100 + 20 t + 20 t + 2 t (2 t)$

Step 4.1.4

Rewrite using the commutative property of multiplication.

$100 + 20 t + 20 t + 2 \cdot 2 t \cdot t$

Step 4.1.5

Multiply $t$ by $t$ by adding the exponents.

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Step 4.1.5.1

Move $t$ .

$100 + 20 t + 20 t + 2 \cdot 2 (t \cdot t)$

Step 4.1.5.2

Multiply $t$ by $t$ .

$100 + 20 t + 20 t + 2 \cdot 2 t^{2}$

Step 4.1.6

Multiply $2$ by $2$ .

$100 + 20 t + 20 t + 4 t^{2}$

Step 4.2

Add $20 t$ and $20 t$ .

$100 + 40 t + 4 t^{2}$

Step 5

Move $100$ .

$40 t + 4 t^{2} + 100$

Step 6

Reorder $40 t$ and $4 t^{2}$ .

$4 t^{2} + 40 t + 100$