Simplify (4x+7)(x-2)(x-1)(x-1)

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

Step 1

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

Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

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

Step 2

Simplify and combine like terms.

Simplify each term.

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

Move $x$ .

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

Multiply $x$ by $x$ .

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

Multiply $- 2$ by $4$ .

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

Multiply $7$ by $- 2$ .

$(4 x^{2} - 8 x + 7 x - 14) (x - 1) (x - 1)$

Add $- 8 x$ and $7 x$ .

$(4 x^{2} - x - 14) (x - 1) (x - 1)$

Step 3

Expand $(4 x^{2} - x - 14) (x - 1)$ by multiplying each term in the first expression by each term in the second expression.

$(4 x^{2} x + 4 x^{2} \cdot - 1 - x \cdot x - x \cdot - 1 - 14 x - 14 \cdot - 1) (x - 1)$

Step 4

Simplify terms.

Simplify each term.

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

Move $x$ .

$(4 (x \cdot x^{2}) + 4 x^{2} \cdot - 1 - x \cdot x - x \cdot - 1 - 14 x - 14 \cdot - 1) (x - 1)$

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

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

$(4 (x^{1} x^{2}) + 4 x^{2} \cdot - 1 - x \cdot x - x \cdot - 1 - 14 x - 14 \cdot - 1) (x - 1)$

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

$(4 x^{1 + 2} + 4 x^{2} \cdot - 1 - x \cdot x - x \cdot - 1 - 14 x - 14 \cdot - 1) (x - 1)$

Add $1$ and $2$ .

$(4 x^{3} + 4 x^{2} \cdot - 1 - x \cdot x - x \cdot - 1 - 14 x - 14 \cdot - 1) (x - 1)$

Multiply $- 1$ by $4$ .

$(4 x^{3} - 4 x^{2} - x \cdot x - x \cdot - 1 - 14 x - 14 \cdot - 1) (x - 1)$

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

Move $x$ .

$(4 x^{3} - 4 x^{2} - (x \cdot x) - x \cdot - 1 - 14 x - 14 \cdot - 1) (x - 1)$

Multiply $x$ by $x$ .

$(4 x^{3} - 4 x^{2} - x^{2} - x \cdot - 1 - 14 x - 14 \cdot - 1) (x - 1)$

Multiply $- x \cdot - 1$ .

Multiply $- 1$ by $- 1$ .

$(4 x^{3} - 4 x^{2} - x^{2} + 1 x - 14 x - 14 \cdot - 1) (x - 1)$

Multiply $x$ by $1$ .

$(4 x^{3} - 4 x^{2} - x^{2} + x - 14 x - 14 \cdot - 1) (x - 1)$

Multiply $- 14$ by $- 1$ .

$(4 x^{3} - 4 x^{2} - x^{2} + x - 14 x + 14) (x - 1)$

Simplify by adding terms.

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

$(4 x^{3} - 5 x^{2} + x - 14 x + 14) (x - 1)$

Subtract $14 x$ from $x$ .

$(4 x^{3} - 5 x^{2} - 13 x + 14) (x - 1)$

Step 5

Expand $(4 x^{3} - 5 x^{2} - 13 x + 14) (x - 1)$ by multiplying each term in the first expression by each term in the second expression.

$4 x^{3} x + 4 x^{3} \cdot - 1 - 5 x^{2} x - 5 x^{2} \cdot - 1 - 13 x \cdot x - 13 x \cdot - 1 + 14 x + 14 \cdot - 1$

Step 6

Simplify terms.

Simplify each term.

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

Move $x$ .

$4 (x \cdot x^{3}) + 4 x^{3} \cdot - 1 - 5 x^{2} x - 5 x^{2} \cdot - 1 - 13 x \cdot x - 13 x \cdot - 1 + 14 x + 14 \cdot - 1$

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

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

$4 (x^{1} x^{3}) + 4 x^{3} \cdot - 1 - 5 x^{2} x - 5 x^{2} \cdot - 1 - 13 x \cdot x - 13 x \cdot - 1 + 14 x + 14 \cdot - 1$

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

$4 x^{1 + 3} + 4 x^{3} \cdot - 1 - 5 x^{2} x - 5 x^{2} \cdot - 1 - 13 x \cdot x - 13 x \cdot - 1 + 14 x + 14 \cdot - 1$

Add $1$ and $3$ .

$4 x^{4} + 4 x^{3} \cdot - 1 - 5 x^{2} x - 5 x^{2} \cdot - 1 - 13 x \cdot x - 13 x \cdot - 1 + 14 x + 14 \cdot - 1$

Multiply $- 1$ by $4$ .

$4 x^{4} - 4 x^{3} - 5 x^{2} x - 5 x^{2} \cdot - 1 - 13 x \cdot x - 13 x \cdot - 1 + 14 x + 14 \cdot - 1$

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

Move $x$ .

$4 x^{4} - 4 x^{3} - 5 (x \cdot x^{2}) - 5 x^{2} \cdot - 1 - 13 x \cdot x - 13 x \cdot - 1 + 14 x + 14 \cdot - 1$

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

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

$4 x^{4} - 4 x^{3} - 5 (x^{1} x^{2}) - 5 x^{2} \cdot - 1 - 13 x \cdot x - 13 x \cdot - 1 + 14 x + 14 \cdot - 1$

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

$4 x^{4} - 4 x^{3} - 5 x^{1 + 2} - 5 x^{2} \cdot - 1 - 13 x \cdot x - 13 x \cdot - 1 + 14 x + 14 \cdot - 1$

Add $1$ and $2$ .

$4 x^{4} - 4 x^{3} - 5 x^{3} - 5 x^{2} \cdot - 1 - 13 x \cdot x - 13 x \cdot - 1 + 14 x + 14 \cdot - 1$

Multiply $- 1$ by $- 5$ .

$4 x^{4} - 4 x^{3} - 5 x^{3} + 5 x^{2} - 13 x \cdot x - 13 x \cdot - 1 + 14 x + 14 \cdot - 1$

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

Move $x$ .

$4 x^{4} - 4 x^{3} - 5 x^{3} + 5 x^{2} - 13 (x \cdot x) - 13 x \cdot - 1 + 14 x + 14 \cdot - 1$

Multiply $x$ by $x$ .

$4 x^{4} - 4 x^{3} - 5 x^{3} + 5 x^{2} - 13 x^{2} - 13 x \cdot - 1 + 14 x + 14 \cdot - 1$

Multiply $- 1$ by $- 13$ .

$4 x^{4} - 4 x^{3} - 5 x^{3} + 5 x^{2} - 13 x^{2} + 13 x + 14 x + 14 \cdot - 1$

Multiply $14$ by $- 1$ .

$4 x^{4} - 4 x^{3} - 5 x^{3} + 5 x^{2} - 13 x^{2} + 13 x + 14 x - 14$

Simplify by adding terms.

Subtract $5 x^{3}$ from $- 4 x^{3}$ .

$4 x^{4} - 9 x^{3} + 5 x^{2} - 13 x^{2} + 13 x + 14 x - 14$

Subtract $13 x^{2}$ from $5 x^{2}$ .

$4 x^{4} - 9 x^{3} - 8 x^{2} + 13 x + 14 x - 14$

Add $13 x$ and $14 x$ .

$4 x^{4} - 9 x^{3} - 8 x^{2} + 27 x - 14$

Simplify (4x+7)(x-2)(x-1)(x-1)

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