Write in Standard Form (x+1)(x-2)(x+4)(3x+7)

$(x + 1) (x - 2) (x + 4) (3 x + 7)$

To write a polynomial in standard form, simplify and then arrange the terms in descending order.

$a x^{2} + b x + c$

Expand $(x + 1) (x - 2)$ using the FOIL Method.

Apply the distributive property.

$(x (x - 2) + 1 (x - 2)) (x + 4) (3 x + 7)$

Apply the distributive property.

$(x \cdot x + x \cdot - 2 + 1 (x - 2)) (x + 4) (3 x + 7)$

Apply the distributive property.

$(x \cdot x + x \cdot - 2 + 1 x + 1 \cdot - 2) (x + 4) (3 x + 7)$

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

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

Move $- 2$ to the left of $x$ .

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

Multiply $x$ by $1$ .

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

Multiply $- 2$ by $1$ .

$(x^{2} - 2 x + x - 2) (x + 4) (3 x + 7)$

Add $- 2 x$ and $x$ .

$(x^{2} - x - 2) (x + 4) (3 x + 7)$

Expand $(x^{2} - x - 2) (x + 4)$ by multiplying each term in the first expression by each term in the second expression.

$(x^{2} x + x^{2} \cdot 4 - x \cdot x - x \cdot 4 - 2 x - 2 \cdot 4) (3 x + 7)$

Simplify terms.

Simplify each term.

Multiply $x^{2}$ by $x$ by adding the exponents.

Multiply $x^{2}$ by $x$ .

Raise $x$ to the power of $1$ .

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

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

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

Add $2$ and $1$ .

$(x^{3} + x^{2} \cdot 4 - x \cdot x - x \cdot 4 - 2 x - 2 \cdot 4) (3 x + 7)$

Move $4$ to the left of $x^{2}$ .

$(x^{3} + 4 \cdot x^{2} - x \cdot x - x \cdot 4 - 2 x - 2 \cdot 4) (3 x + 7)$

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

Move $x$ .

$(x^{3} + 4 x^{2} - (x \cdot x) - x \cdot 4 - 2 x - 2 \cdot 4) (3 x + 7)$

Multiply $x$ by $x$ .

$(x^{3} + 4 x^{2} - x^{2} - x \cdot 4 - 2 x - 2 \cdot 4) (3 x + 7)$

Multiply $4$ by $- 1$ .

$(x^{3} + 4 x^{2} - x^{2} - 4 x - 2 x - 2 \cdot 4) (3 x + 7)$

Multiply $- 2$ by $4$ .

$(x^{3} + 4 x^{2} - x^{2} - 4 x - 2 x - 8) (3 x + 7)$

Simplify by adding terms.

Subtract $x^{2}$ from $4 x^{2}$ .

$(x^{3} + 3 x^{2} - 4 x - 2 x - 8) (3 x + 7)$

Subtract $2 x$ from $- 4 x$ .

$(x^{3} + 3 x^{2} - 6 x - 8) (3 x + 7)$

Expand $(x^{3} + 3 x^{2} - 6 x - 8) (3 x + 7)$ by multiplying each term in the first expression by each term in the second expression.

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

Simplify terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

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

Multiply $x^{3}$ by $x$ by adding the exponents.

Move $x$ .

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

Multiply $x$ by $x^{3}$ .

Raise $x$ to the power of $1$ .

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

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

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

Add $1$ and $3$ .

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

Move $7$ to the left of $x^{3}$ .

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

Rewrite using the commutative property of multiplication.

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

Multiply $x^{2}$ by $x$ by adding the exponents.

Move $x$ .

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

Multiply $x$ by $x^{2}$ .

Raise $x$ to the power of $1$ .

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

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

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

Add $1$ and $2$ .

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

Multiply $3$ by $3$ .

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

Multiply $7$ by $3$ .

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

Rewrite using the commutative property of multiplication.

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

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

Move $x$ .

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

Multiply $x$ by $x$ .

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

Multiply $- 6$ by $3$ .

$3 x^{4} + 7 x^{3} + 9 x^{3} + 21 x^{2} - 18 x^{2} - 6 x \cdot 7 - 8 (3 x) - 8 \cdot 7$

Multiply $7$ by $- 6$ .

$3 x^{4} + 7 x^{3} + 9 x^{3} + 21 x^{2} - 18 x^{2} - 42 x - 8 (3 x) - 8 \cdot 7$

Multiply $3$ by $- 8$ .

$3 x^{4} + 7 x^{3} + 9 x^{3} + 21 x^{2} - 18 x^{2} - 42 x - 24 x - 8 \cdot 7$

Multiply $- 8$ by $7$ .

$3 x^{4} + 7 x^{3} + 9 x^{3} + 21 x^{2} - 18 x^{2} - 42 x - 24 x - 56$

Simplify by adding terms.

Add $7 x^{3}$ and $9 x^{3}$ .

$3 x^{4} + 16 x^{3} + 21 x^{2} - 18 x^{2} - 42 x - 24 x - 56$

Subtract $18 x^{2}$ from $21 x^{2}$ .

$3 x^{4} + 16 x^{3} + 3 x^{2} - 42 x - 24 x - 56$

Subtract $24 x$ from $- 42 x$ .

$3 x^{4} + 16 x^{3} + 3 x^{2} - 66 x - 56$

Write in Standard Form (x+1)(x-2)(x+4)(3x+7)

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