Question

im2: u1, quiz 3 (mild)
per: 3
name: hisdolio

1. simplify (*hint: combine the like terms. not multiplying!!):

a) $(2x + 2)+(3x + 4) = $
b) $(2x - 7)-(1x + 5) = $

1. multiply the factors (hint: *use area model):

a) $(x + 3)(x - 5) = $
b) $(x - 2)(3x + 7) = $

Explanation:

Step1: Remove parentheses (addition)

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

Step2: Combine like x terms

$2x + 3x + 2 + 4 = 5x + 2 + 4$

Step3: Combine constant terms

$5x + (2 + 4) = 5x + 6$

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Step1: Distribute negative sign

$(2x - 7) - (1x + 5) = 2x - 7 - x - 5$

Step2: Combine like x terms

$2x - x - 7 - 5 = x - 7 - 5$

Step3: Combine constant terms

$x + (-7 - 5) = x - 12$

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Step1: Use area model to expand

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

Step2: Calculate each term

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

Step3: Combine like x terms

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

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Step1: Use area model to expand

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

Step2: Calculate each term

$= 3x^2 + 7x - 6x - 14$

Step3: Combine like x terms

$3x^2 + (7x - 6x) - 14 = 3x^2 + x - 14$

Answer:

a) $5x + 6$
b) $x - 12$
a) $x^2 - 2x - 15$
b) $3x^2 + x - 14$