Expand the Trigonometric Expression (5a+2)(a+4)

$(5 a + 2) (a + 4)$

Step 1

Expand $(5 a + 2) (a + 4)$ using the FOIL Method.

Apply the distributive property.

$5 a (a + 4) + 2 (a + 4)$

Apply the distributive property.

$5 a \cdot a + 5 a \cdot 4 + 2 (a + 4)$

Apply the distributive property.

$5 a \cdot a + 5 a \cdot 4 + 2 a + 2 \cdot 4$

$5 a \cdot a + 5 a \cdot 4 + 2 a + 2 \cdot 4$

Step 2

Simplify and combine like terms.

Simplify each term.

Multiply $a$ by $a$ by adding the exponents.

Move $a$ .

$5 (a \cdot a) + 5 a \cdot 4 + 2 a + 2 \cdot 4$

Multiply $a$ by $a$ .

$5 a^{2} + 5 a \cdot 4 + 2 a + 2 \cdot 4$

$5 a^{2} + 5 a \cdot 4 + 2 a + 2 \cdot 4$

Multiply $4$ by $5$ .

$5 a^{2} + 20 a + 2 a + 2 \cdot 4$

Multiply $2$ by $4$ .

$5 a^{2} + 20 a + 2 a + 8$

$5 a^{2} + 20 a + 2 a + 8$

Add $20 a$ and $2 a$ .

$5 a^{2} + 22 a + 8$

$5 a^{2} + 22 a + 8$

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