Pre-Algebra Examples

$- 30$ , $0 t^{2} + 1$ , $800$ , $0 t + 35$ , $0$

Step 1

Add $- 30 + 0 t^{2} + 1 + 800 + 0 t + 35$ and $0$ .

$- 30 + 0 t^{2} + 1 + 800 + 0 t + 35$

Step 2

Add $- 30$ and $1$ .

$0 t^{2} - 29 + 800 + 0 t + 35$

Step 3

Add $- 29$ and $800$ .

$0 t^{2} + 771 + 0 t + 35$

Step 4

Add $771$ and $35$ .

$0 t^{2} + 0 t + 806$

Step 5

Factor $806$ out of $0 t^{2} + 0 t + 806$ .

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Step 5.1

Factor $806$ out of $0 t^{2}$ .

$806 (0 t^{2}) + 0 t + 806$

Step 5.2

Factor $806$ out of $0 t$ .

$806 (0 t^{2}) + 806 (0 t) + 806$

Step 5.3

Factor $806$ out of $806$ .

$806 (0 t^{2}) + 806 (0 t) + 806 (1)$

Step 5.4

Factor $806$ out of $806 (0 t^{2}) + 806 (0 t)$ .

$806 (0 t^{2} + 0 t) + 806 (1)$

Step 5.5

Factor $806$ out of $806 (0 t^{2} + 0 t) + 806 (1)$ .

$806 (0 t^{2} + 0 t + 1)$

Step 6

Factor using the perfect square rule.

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Step 6.1

Rewrite $0 t^{2}$ as ${(0 t)}^{2}$ .

$806 ({(0 t)}^{2} + 0 t + 1)$

Step 6.2

Rewrite $1$ as $1^{2}$ .

$806 ({(0 t)}^{2} + 0 t + 1^{2})$

Step 6.3

Check that the middle term is two times the product of the numbers being squared in the first term and third term.

$0 t = 2 \cdot (0 t) \cdot 1$

Step 6.4

Rewrite the polynomial.

$806 ({(0 t)}^{2} + 2 \cdot (0 t) \cdot 1 + 1^{2})$

Step 6.5

Factor using the perfect square trinomial rule $a^{2} + 2 a b + b^{2} = {(a + b)}^{2}$ , where $a = 0 t$ and $b = 1$ .

$806 {(0 t + 1)}^{2}$

Step 7

Multiply $0$ by $t$ .

$806 {(0 + 1)}^{2}$

Step 8

Add $0$ and $1$ .

$806 \cdot 1^{2}$