Algebra Examples

$(6 x^{2} + 2 x - 9) + (8 x^{2} - 5 x + 1) - (3 x - 4) (7 x + 2)$

Step 1

Remove parentheses.

$6 x^{2} + 2 x - 9 + 8 x^{2} - 5 x + 1 - (3 x - 4) (7 x + 2)$

Step 2

Simplify each term.

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Step 2.1

Apply the distributive property.

$6 x^{2} + 2 x - 9 + 8 x^{2} - 5 x + 1 + (- (3 x) - - 4) (7 x + 2)$

Step 2.2

Multiply $3$ by $- 1$ .

$6 x^{2} + 2 x - 9 + 8 x^{2} - 5 x + 1 + (- 3 x - - 4) (7 x + 2)$

Step 2.3

Multiply $- 1$ by $- 4$ .

$6 x^{2} + 2 x - 9 + 8 x^{2} - 5 x + 1 + (- 3 x + 4) (7 x + 2)$

Step 2.4

Expand $(- 3 x + 4) (7 x + 2)$ using the FOIL Method.

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Step 2.4.1

Apply the distributive property.

$6 x^{2} + 2 x - 9 + 8 x^{2} - 5 x + 1 - 3 x (7 x + 2) + 4 (7 x + 2)$

Step 2.4.2

Apply the distributive property.

$6 x^{2} + 2 x - 9 + 8 x^{2} - 5 x + 1 - 3 x (7 x) - 3 x \cdot 2 + 4 (7 x + 2)$

Step 2.4.3

Apply the distributive property.

$6 x^{2} + 2 x - 9 + 8 x^{2} - 5 x + 1 - 3 x (7 x) - 3 x \cdot 2 + 4 (7 x) + 4 \cdot 2$

Step 2.5

Simplify and combine like terms.

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Step 2.5.1

Simplify each term.

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Step 2.5.1.1

Rewrite using the commutative property of multiplication.

$6 x^{2} + 2 x - 9 + 8 x^{2} - 5 x + 1 - 3 \cdot 7 x \cdot x - 3 x \cdot 2 + 4 (7 x) + 4 \cdot 2$

Step 2.5.1.2

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

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Step 2.5.1.2.1

Move $x$ .

$6 x^{2} + 2 x - 9 + 8 x^{2} - 5 x + 1 - 3 \cdot 7 (x \cdot x) - 3 x \cdot 2 + 4 (7 x) + 4 \cdot 2$

Step 2.5.1.2.2

Multiply $x$ by $x$ .

$6 x^{2} + 2 x - 9 + 8 x^{2} - 5 x + 1 - 3 \cdot 7 x^{2} - 3 x \cdot 2 + 4 (7 x) + 4 \cdot 2$

Step 2.5.1.3

Multiply $- 3$ by $7$ .

$6 x^{2} + 2 x - 9 + 8 x^{2} - 5 x + 1 - 21 x^{2} - 3 x \cdot 2 + 4 (7 x) + 4 \cdot 2$

Step 2.5.1.4

Multiply $2$ by $- 3$ .

$6 x^{2} + 2 x - 9 + 8 x^{2} - 5 x + 1 - 21 x^{2} - 6 x + 4 (7 x) + 4 \cdot 2$

Step 2.5.1.5

Multiply $7$ by $4$ .

$6 x^{2} + 2 x - 9 + 8 x^{2} - 5 x + 1 - 21 x^{2} - 6 x + 28 x + 4 \cdot 2$

Step 2.5.1.6

Multiply $4$ by $2$ .

$6 x^{2} + 2 x - 9 + 8 x^{2} - 5 x + 1 - 21 x^{2} - 6 x + 28 x + 8$

Step 2.5.2

Add $- 6 x$ and $28 x$ .

$6 x^{2} + 2 x - 9 + 8 x^{2} - 5 x + 1 - 21 x^{2} + 22 x + 8$

Step 3

Simplify by adding terms.

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Step 3.1

Add $6 x^{2}$ and $8 x^{2}$ .

$14 x^{2} + 2 x - 9 - 5 x + 1 - 21 x^{2} + 22 x + 8$

Step 3.2

Subtract $21 x^{2}$ from $14 x^{2}$ .

$- 7 x^{2} + 2 x - 9 - 5 x + 1 + 22 x + 8$

Step 3.3

Subtract $5 x$ from $2 x$ .

$- 7 x^{2} - 3 x - 9 + 1 + 22 x + 8$

Step 3.4

Add $- 3 x$ and $22 x$ .

$- 7 x^{2} + 19 x - 9 + 1 + 8$

Step 3.5

Add $- 9$ and $1$ .

$- 7 x^{2} + 19 x - 8 + 8$

Step 3.6

Combine the opposite terms in $- 7 x^{2} + 19 x - 8 + 8$ .

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Step 3.6.1

Add $- 8$ and $8$ .

$- 7 x^{2} + 19 x + 0$

Step 3.6.2

Add $- 7 x^{2} + 19 x$ and $0$ .

$- 7 x^{2} + 19 x$