Question

do you know how?
simplify each product.

1. $(x + 3)(x + 6)$
2. $(2x - 5)(x + 3)$
3. $(x + 2)(x^2 + 3x - 4)$
4. a rectangle has length $x + 5$ and width $x - 3$. what is the area of the rectangle?

write your answer as a polynomial in standard form.

Explanation:

Step1: Apply distributive property (FOIL)

$(x+3)(x+6) = x\cdot x + x\cdot6 + 3\cdot x + 3\cdot6$

Step2: Calculate and combine like terms

$=x^2 + 6x + 3x + 18 = x^2 + 9x + 18$

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Step1: Apply distributive property (FOIL)

$(2x-5)(x+3) = 2x\cdot x + 2x\cdot3 -5\cdot x -5\cdot3$

Step2: Calculate and combine like terms

$=2x^2 + 6x -5x -15 = 2x^2 + x -15$

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Step1: Distribute binomial to trinomial

$(x+2)(x^2+3x-4) = x(x^2+3x-4) + 2(x^2+3x-4)$

Step2: Expand each term

$=x^3 + 3x^2 -4x + 2x^2 + 6x -8$

Step3: Combine like terms

$=x^3 + (3x^2+2x^2) + (-4x+6x) -8 = x^3 + 5x^2 + 2x -8$

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Step1: Use area formula for rectangle

$\text{Area} = \text{length} \times \text{width} = (x+5)(x-3)$

Step2: Apply distributive property (FOIL)

$=x\cdot x + x\cdot(-3) +5\cdot x +5\cdot(-3)$

Step3: Calculate and combine like terms

$=x^2 -3x +5x -15 = x^2 + 2x -15$

Answer:

1. $x^2 + 9x + 18$
2. $2x^2 + x - 15$
3. $x^3 + 5x^2 + 2x - 8$
4. $x^2 + 2x - 15$