Basic Math Examples

${(2 \sin (A) \cos (B))}^{2} + {(2 \sin (A) \sin (B))}^{2} + {(2 \cos (A))}^{2}$

Step 1

Simplify each term.

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Step 1.1

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

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Step 1.1.1

Apply the product rule to $2 \sin (A) \cos (B)$ .

${(2 \sin (A))}^{2} \cos^{2} (B) + {(2 \sin (A) \sin (B))}^{2} + {(2 \cos (A))}^{2}$

Step 1.1.2

Apply the product rule to $2 \sin (A)$ .

$2^{2} \sin^{2} (A) \cos^{2} (B) + {(2 \sin (A) \sin (B))}^{2} + {(2 \cos (A))}^{2}$

Step 1.2

Raise $2$ to the power of $2$ .

$4 \sin^{2} (A) \cos^{2} (B) + {(2 \sin (A) \sin (B))}^{2} + {(2 \cos (A))}^{2}$

Step 1.3

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

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Step 1.3.1

Apply the product rule to $2 \sin (A) \sin (B)$ .

$4 \sin^{2} (A) \cos^{2} (B) + {(2 \sin (A))}^{2} \sin^{2} (B) + {(2 \cos (A))}^{2}$

Step 1.3.2

Apply the product rule to $2 \sin (A)$ .

$4 \sin^{2} (A) \cos^{2} (B) + 2^{2} \sin^{2} (A) \sin^{2} (B) + {(2 \cos (A))}^{2}$

Step 1.4

Raise $2$ to the power of $2$ .

$4 \sin^{2} (A) \cos^{2} (B) + 4 \sin^{2} (A) \sin^{2} (B) + {(2 \cos (A))}^{2}$

Step 1.5

Apply the product rule to $2 \cos (A)$ .

$4 \sin^{2} (A) \cos^{2} (B) + 4 \sin^{2} (A) \sin^{2} (B) + 2^{2} \cos^{2} (A)$

Step 1.6

Raise $2$ to the power of $2$ .

$4 \sin^{2} (A) \cos^{2} (B) + 4 \sin^{2} (A) \sin^{2} (B) + 4 \cos^{2} (A)$

Step 2

Simplify with factoring out.

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Step 2.1

Factor $4 \sin^{2} (A)$ out of $4 \sin^{2} (A) \cos^{2} (B)$ .

$4 \sin^{2} (A) (\cos^{2} (B)) + 4 \sin^{2} (A) \sin^{2} (B) + 4 \cos^{2} (A)$

Step 2.2

Factor $4 \sin^{2} (A)$ out of $4 \sin^{2} (A) \sin^{2} (B)$ .

$4 \sin^{2} (A) (\cos^{2} (B)) + 4 \sin^{2} (A) (\sin^{2} (B)) + 4 \cos^{2} (A)$

Step 2.3

Factor $4 \sin^{2} (A)$ out of $4 \sin^{2} (A) (\cos^{2} (B)) + 4 \sin^{2} (A) (\sin^{2} (B))$ .

$4 \sin^{2} (A) (\cos^{2} (B) + \sin^{2} (B)) + 4 \cos^{2} (A)$

Step 3

Rearrange terms.

$4 \sin^{2} (A) (\sin^{2} (B) + \cos^{2} (B)) + 4 \cos^{2} (A)$

Step 4

Apply pythagorean identity.

$4 \sin^{2} (A) \cdot 1 + 4 \cos^{2} (A)$

Step 5

Simplify with factoring out.

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Step 5.1

Multiply $4$ by $1$ .

$4 \sin^{2} (A) + 4 \cos^{2} (A)$

Step 5.2

Factor $4$ out of $4 \sin^{2} (A)$ .

$4 (\sin^{2} (A)) + 4 \cos^{2} (A)$

Step 5.3

Factor $4$ out of $4 \cos^{2} (A)$ .

$4 (\sin^{2} (A)) + 4 (\cos^{2} (A))$

Step 5.4

Factor $4$ out of $4 (\sin^{2} (A)) + 4 (\cos^{2} (A))$ .

$4 (\sin^{2} (A) + \cos^{2} (A))$

Step 6

Apply pythagorean identity.

$4 \cdot 1$

Step 7

Multiply $4$ by $1$ .

$4$