Algebra Examples

${(k t + p)}^{2} - 2 p (k t + p) + 7$

Step 1

Simplify each term.

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Step 1.1

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

$(k t + p) (k t + p) - 2 p (k t + p) + 7$

Step 1.2

Expand $(k t + p) (k t + p)$ using the FOIL Method.

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Step 1.2.1

Apply the distributive property.

$k t (k t + p) + p (k t + p) - 2 p (k t + p) + 7$

Step 1.2.2

Apply the distributive property.

$k t (k t) + k t p + p (k t + p) - 2 p (k t + p) + 7$

Step 1.2.3

Apply the distributive property.

$k t (k t) + k t p + p (k t) + p \cdot p - 2 p (k t + p) + 7$

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 $k$ by $k$ by adding the exponents.

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Step 1.3.1.1.1

Move $k$ .

$k \cdot k t \cdot t + k t p + p (k t) + p \cdot p - 2 p (k t + p) + 7$

Step 1.3.1.1.2

Multiply $k$ by $k$ .

$k^{2} t \cdot t + k t p + p (k t) + p \cdot p - 2 p (k t + p) + 7$

Step 1.3.1.2

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

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Step 1.3.1.2.1

Move $t$ .

$k^{2} (t \cdot t) + k t p + p (k t) + p \cdot p - 2 p (k t + p) + 7$

Step 1.3.1.2.2

Multiply $t$ by $t$ .

$k^{2} t^{2} + k t p + p (k t) + p \cdot p - 2 p (k t + p) + 7$

Step 1.3.1.3

Multiply $p$ by $p$ .

$k^{2} t^{2} + k t p + p k t + p^{2} - 2 p (k t + p) + 7$

Step 1.3.2

Reorder $p$ and $k$ .

$k^{2} t^{2} + k p t + k p t + p^{2} - 2 p (k t + p) + 7$

Step 1.3.3

Add $k p t$ and $k p t$ .

$k^{2} t^{2} + 2 k p t + p^{2} - 2 p (k t + p) + 7$

Step 1.4

Apply the distributive property.

$k^{2} t^{2} + 2 k p t + p^{2} - 2 p (k t) - 2 p \cdot p + 7$

Step 1.5

Multiply $p$ by $p$ by adding the exponents.

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Step 1.5.1

Move $p$ .

$k^{2} t^{2} + 2 k p t + p^{2} - 2 p k t - 2 (p \cdot p) + 7$

Step 1.5.2

Multiply $p$ by $p$ .

$k^{2} t^{2} + 2 k p t + p^{2} - 2 p k t - 2 p^{2} + 7$

Step 2

Simplify by adding terms.

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Step 2.1

Combine the opposite terms in $k^{2} t^{2} + 2 k p t + p^{2} - 2 p k t - 2 p^{2} + 7$ .

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Step 2.1.1

Reorder the factors in the terms $2 k p t$ and $- 2 p k t$ .

$k^{2} t^{2} + 2 k p t + p^{2} - 2 k p t - 2 p^{2} + 7$

Step 2.1.2

Subtract $2 k p t$ from $2 k p t$ .

$k^{2} t^{2} + p^{2} + 0 - 2 p^{2} + 7$

Step 2.1.3

Add $k^{2} t^{2} + p^{2}$ and $0$ .

$k^{2} t^{2} + p^{2} - 2 p^{2} + 7$

Step 2.2

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

$k^{2} t^{2} - p^{2} + 7$