Basic Math Examples

$6 {(r - 5)}^{2} + 1$

Step 1

Simplify each term.

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Step 1.1

Rewrite ${(r - 5)}^{2}$ as $(r - 5) (r - 5)$ .

$6 ((r - 5) (r - 5)) + 1$

Step 1.2

Expand $(r - 5) (r - 5)$ using the FOIL Method.

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Step 1.2.1

Apply the distributive property.

$6 (r (r - 5) - 5 (r - 5)) + 1$

Step 1.2.2

Apply the distributive property.

$6 (r \cdot r + r \cdot - 5 - 5 (r - 5)) + 1$

Step 1.2.3

Apply the distributive property.

$6 (r \cdot r + r \cdot - 5 - 5 r - 5 \cdot - 5) + 1$

$6 (r \cdot r + r \cdot - 5 - 5 r - 5 \cdot - 5) + 1$

Step 1.3

Simplify and combine like terms.

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Step 1.3.1

Simplify each term.

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Step 1.3.1.1

Multiply $r$ by $r$ .

$6 (r^{2} + r \cdot - 5 - 5 r - 5 \cdot - 5) + 1$

Step 1.3.1.2

Move $- 5$ to the left of $r$ .

$6 (r^{2} - 5 \cdot r - 5 r - 5 \cdot - 5) + 1$

Step 1.3.1.3

Multiply $- 5$ by $- 5$ .

$6 (r^{2} - 5 r - 5 r + 25) + 1$

$6 (r^{2} - 5 r - 5 r + 25) + 1$

Step 1.3.2

Subtract $5 r$ from $- 5 r$ .

$6 (r^{2} - 10 r + 25) + 1$

$6 (r^{2} - 10 r + 25) + 1$

Step 1.4

Apply the distributive property.

$6 r^{2} + 6 (- 10 r) + 6 \cdot 25 + 1$

Step 1.5

Simplify.

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Step 1.5.1

Multiply $- 10$ by $6$ .

$6 r^{2} - 60 r + 6 \cdot 25 + 1$

Step 1.5.2

Multiply $6$ by $25$ .

$6 r^{2} - 60 r + 150 + 1$

$6 r^{2} - 60 r + 150 + 1$

$6 r^{2} - 60 r + 150 + 1$

Step 2

Add $150$ and $1$ .

$6 r^{2} - 60 r + 151$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$