Question

problem 3 using foil got it? what is a simpler form of each product? use the foil method. a. (3x - 4)(x + 2) b. (n - 6)(4n - 7) c. (2p² + 3)(2p - 5) plan how can a diagram help you multiply two binomials?

Explanation:

Part a:

Step1: Apply FOIL (First terms)

Multiply first terms of each binomial:
$3x \cdot x = 3x^2$

Step2: Apply FOIL (Outer terms)

Multiply outer terms of the binomials:
$3x \cdot 2 = 6x$

Step3: Apply FOIL (Inner terms)

Multiply inner terms of the binomials:
$-4 \cdot x = -4x$

Step4: Apply FOIL (Last terms)

Multiply last terms of each binomial:
$-4 \cdot 2 = -8$

Step5: Combine like terms

Sum all terms and simplify:
$3x^2 + 6x - 4x - 8 = 3x^2 + 2x - 8$

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Part b:

Step1: Apply FOIL (First terms)

Multiply first terms of each binomial:
$n \cdot 4n = 4n^2$

Step2: Apply FOIL (Outer terms)

Multiply outer terms of the binomials:
$n \cdot (-7) = -7n$

Step3: Apply FOIL (Inner terms)

Multiply inner terms of the binomials:
$-6 \cdot 4n = -24n$

Step4: Apply FOIL (Last terms)

Multiply last terms of each binomial:
$-6 \cdot (-7) = 42$

Step5: Combine like terms

Sum all terms and simplify:
$4n^2 -7n -24n +42 = 4n^2 -31n +42$

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Part c:

Step1: Apply FOIL (First terms)

Multiply first terms of each binomial:
$2p^2 \cdot 2p = 4p^3$

Step2: Apply FOIL (Outer terms)

Multiply outer terms of the binomials:
$2p^2 \cdot (-5) = -10p^2$

Step3: Apply FOIL (Inner terms)

Multiply inner terms of the binomials:
$3 \cdot 2p = 6p$

Step4: Apply FOIL (Last terms)

Multiply last terms of each binomial:
$3 \cdot (-5) = -15$

Step5: Combine like terms (no like terms left to combine)

Sum all terms:
$4p^3 -10p^2 +6p -15$

Answer:

a. $3x^2 + 2x - 8$
b. $4n^2 - 31n + 42$
c. $4p^3 - 10p^2 + 6p - 15$