To expand the expression (x+3)(x+2), we use the distributive property, often remembered by the FOIL method (First, Outer, Inner, Last). Step 1: Multiply the First terms of each binomial. x × x = x² Step 2: Multiply the Outer terms of the expression. x × 2 = 2x Step 3: Multiply the Inner terms of the expression. 3 × x = 3x Step 4: Multiply the Last terms of each binomial. 3 × 2 = 6 Step 5: Add all these products together. x² + 2x + 3x + 6 Step 6: Combine the like terms (2x and 3x). x² + (2x + 3x) + 6 x² + 5x + 6 Comparing this result with the given options: A. x²+5x+6 B. x²+6x+5 C. x²+3x+2 D. x²+2x+3 The expanded expression matches option A. The final answer is A. x²+5x+6.

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Expand: (x+3)(x+2)

July 4, 2026Mathematics

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Step-by-step solution

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To expand the expression $(x+3)(x+2)$ , we use the distributive property, often remembered by the FOIL method (First, Outer, Inner, Last).

Multiply the First terms of each binomial.
$x \times x = x^2$
Multiply the Outer terms of the expression.
$x \times 2 = 2x$
Multiply the Inner terms of the expression.
$3 \times x = 3x$
Multiply the Last terms of each binomial.
$3 \times 2 = 6$
Add all these products together.
$x^2 + 2x + 3x + 6$
Combine the like terms ($2x$ and $3x$).
$x^2 + (2x + 3x) + 6$ $x^2 + 5x + 6$
Comparing this result with the given options:
A. $x^2+5x+6$
B. $x^2+6x+5$
C. $x^2+3x+2$
D. $x^2+2x+3$

The expanded expression matches option A.

The final answer is $\boxed{\text{A. } x^2+5x+6}$ .

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Expand: (x+3)(x+2)

Step-by-step solution

Multiply the First terms of each binomial.

Multiply the Outer terms of the expression.

Multiply the Inner terms of the expression.

Multiply the Last terms of each binomial.

Add all these products together.

Combine the like terms ($2x$ and $3x$).

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