Simplify (x-7)(2x+3)

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

Step 1

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

Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

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

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

Step 2

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

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

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

Move $x$ .

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

Multiply $x$ by $x$ .

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

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

Move $3$ to the left of $x$ .

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

Multiply $2$ by $- 7$ .

$2 x^{2} + 3 x - 14 x - 7 \cdot 3$

Multiply $- 7$ by $3$ .

$2 x^{2} + 3 x - 14 x - 21$

$2 x^{2} + 3 x - 14 x - 21$

Subtract $14 x$ from $3 x$ .

$2 x^{2} - 11 x - 21$

$2 x^{2} - 11 x - 21$

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