Algebra Examples

$(4 x^{2} + 8 x + 15) + (x^{2} - x - 27) - (x + 5) (x - 7)$

Step 1

Remove parentheses.

$4 x^{2} + 8 x + 15 + x^{2} - x - 27 - (x + 5) (x - 7)$

Step 2

Simplify each term.

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Step 2.1

Apply the distributive property.

$4 x^{2} + 8 x + 15 + x^{2} - x - 27 + (- x - 1 \cdot 5) (x - 7)$

Step 2.2

Multiply $- 1$ by $5$ .

$4 x^{2} + 8 x + 15 + x^{2} - x - 27 + (- x - 5) (x - 7)$

Step 2.3

Expand $(- x - 5) (x - 7)$ using the FOIL Method.

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Step 2.3.1

Apply the distributive property.

$4 x^{2} + 8 x + 15 + x^{2} - x - 27 - x (x - 7) - 5 (x - 7)$

Step 2.3.2

Apply the distributive property.

$4 x^{2} + 8 x + 15 + x^{2} - x - 27 - x \cdot x - x \cdot - 7 - 5 (x - 7)$

Step 2.3.3

Apply the distributive property.

$4 x^{2} + 8 x + 15 + x^{2} - x - 27 - x \cdot x - x \cdot - 7 - 5 x - 5 \cdot - 7$

Step 2.4

Simplify and combine like terms.

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Step 2.4.1

Simplify each term.

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Step 2.4.1.1

Multiply $x$ by $x$ by adding the exponents.

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Step 2.4.1.1.1

Move $x$ .

$4 x^{2} + 8 x + 15 + x^{2} - x - 27 - (x \cdot x) - x \cdot - 7 - 5 x - 5 \cdot - 7$

Step 2.4.1.1.2

Multiply $x$ by $x$ .

$4 x^{2} + 8 x + 15 + x^{2} - x - 27 - x^{2} - x \cdot - 7 - 5 x - 5 \cdot - 7$

Step 2.4.1.2

Multiply $- 7$ by $- 1$ .

$4 x^{2} + 8 x + 15 + x^{2} - x - 27 - x^{2} + 7 x - 5 x - 5 \cdot - 7$

Step 2.4.1.3

Multiply $- 5$ by $- 7$ .

$4 x^{2} + 8 x + 15 + x^{2} - x - 27 - x^{2} + 7 x - 5 x + 35$

Step 2.4.2

Subtract $5 x$ from $7 x$ .

$4 x^{2} + 8 x + 15 + x^{2} - x - 27 - x^{2} + 2 x + 35$

Step 3

Simplify by adding terms.

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Step 3.1

Combine the opposite terms in $4 x^{2} + 8 x + 15 + x^{2} - x - 27 - x^{2} + 2 x + 35$ .

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Step 3.1.1

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

$4 x^{2} + 8 x + 15 - x - 27 + 0 + 2 x + 35$

Step 3.1.2

Add $4 x^{2} + 8 x + 15 - x - 27$ and $0$ .

$4 x^{2} + 8 x + 15 - x - 27 + 2 x + 35$

Step 3.2

Subtract $x$ from $8 x$ .

$4 x^{2} + 7 x + 15 - 27 + 2 x + 35$

Step 3.3

Add $7 x$ and $2 x$ .

$4 x^{2} + 9 x + 15 - 27 + 35$

Step 3.4

Simplify by adding and subtracting.

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Step 3.4.1

Subtract $27$ from $15$ .

$4 x^{2} + 9 x - 12 + 35$

Step 3.4.2

Add $- 12$ and $35$ .

$4 x^{2} + 9 x + 23$