Evaluate (x+a)^2+5(x+a)+4

${(x + a)}^{2} + 5 (x + a) + 4$

Step 1

Rewrite ${(x + a)}^{2}$ as $(x + a) (x + a)$ .

$(x + a) (x + a) + 5 (x + a) + 4$

Step 2

Expand $(x + a) (x + a)$ using the FOIL Method.

Apply the distributive property.

$x (x + a) + a (x + a) + 5 (x + a) + 4$

Apply the distributive property.

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

Apply the distributive property.

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

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

Step 3

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

$x^{2} + x a + a x + a \cdot a + 5 (x + a) + 4$

Multiply $a$ by $a$ .

$x^{2} + x a + a x + a^{2} + 5 (x + a) + 4$

$x^{2} + x a + a x + a^{2} + 5 (x + a) + 4$

Add $x a$ and $a x$ .

Reorder $x$ and $a$ .

$x^{2} + a x + a x + a^{2} + 5 (x + a) + 4$

Add $a x$ and $a x$ .

$x^{2} + 2 a x + a^{2} + 5 (x + a) + 4$

$x^{2} + 2 a x + a^{2} + 5 (x + a) + 4$

$x^{2} + 2 a x + a^{2} + 5 (x + a) + 4$

Step 4

Apply the distributive property.

$x^{2} + 2 a x + a^{2} + 5 x + 5 a + 4$

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