Question 1

Which of the following correctly applies the FOIL method to multiply $$ (j - k)(j - k) $$?

Accepted Answer

$$ j^2$ - 2jk + k^2$ $$

Question 2

Given the polynomials $$ 4m^2$ + n^2$ - 4mn $$ and $$ m^2$ - 5n^2$ - mn $$, what is the product when arranged in descending powers of $$ m $$?

Accepted Answer

$$ 4m^4$ - 8m^3$n - 15m^2$n^2$$ + $$19mn^3$$ - $$5n^4$$ $

Question 3

Which formula is used to quickly square a binomial $$ (A - B) $$?

Accepted Answer

$$ (A - B)^2$ = A^2$ - 2AB + B^2$ $$

Question 4

What is the expanded form of $$ (4m - \frac{1}{5})^2$ $$?

Accepted Answer

$$ 16m^2$ - \frac{8m}{5} + \frac{1}{25} $$

Question 5

A chemical engineer needs to calculate the area of a square plate with side $$ 20m^2$ + 3.2n $$ units. What is the area in expanded form?

Accepted Answer

$$ 400m^4$ + 128m^2$n + 10.24n^2$ $$

Question 6

Which special product rule is used to expand $$ (A + B)(A - B) $$?

Accepted Answer

$$ (A + B)(A - B) = A^2$ - B^2$ $$

Question 7

Expand and simplify $$ (7m + 8n + 6)(7m + 8n - 6) .$$

Accepted Answer

$$ 49m^2$ + 112mn + 64n^2$ - 36 $$

Question 8

A manufacturer wants to factor the polynomial $$ 24p^3$ + 72p^2$ - 32p - 96 . $$What is the completely factored form?

Accepted Answer

$$ 8(3p - 4)(p^2$ + 3) $$

Question 9

Given $$ p^7$ - p^6$ + p^2$ + p $$, what is the greatest common factor (GCF) and the resulting expression after factoring it out?

Accepted Answer

$$ p(p^6$ - p^5$ + p + 1) $$

Question 10

A trinomial $$ 78m^2$ + 120m - 90  is to be $$factored. What is the correct complete factorization?

Accepted Answer

$$ 6(5m - 3)(4m + 5) $$

Question 11

Which of the following is the correct application of the distributive law to multiply $$ (a + b)(c + d) $$?

Accepted Answer

$$ ac + ad + bc + bd $$

Question 12

A biologist is modeling population growth with the expression $$ (x + 2y)^2$ . $$What is the expanded form?

Accepted Answer

$$ x^2$ + 4xy + 4y^2$ $$

Question 13

Which of the following is a correct step in factoring $$ 20m^2$ + 13m - 15 $$?

Accepted Answer

$$ (5m - 3)(4m + 5) $$

Question 14

A student claims that $$ (a + b)^2$ = a^2$ + b^2$ . Is $$this correct? Why or why not?

Accepted Answer

No, because $$ (a + b)^2$ = a^2$ + 2ab + b^2$ $$

Question 15

Which of the following is the result of factoring $$ x^2$ - 9 $$?

Accepted Answer

$$ (x + 3)(x - 3) $$

Question 16

A real-world application: The area of a rectangular garden is given by $$ (l + w)^2$ . If$$ $$ l = 5 $$ meters and $$ w = 3 $$ meters, what is the area?

Accepted Answer

$$ 64 $$ square meters

Question 17

Which of the following is the correct factorization of $$ x^2$ + 6x + 9 $$?

Accepted Answer

$$ (x + 3)^2$ $$

Question 18

A physics problem involves the difference of squares: $$ (v + u)(v - u) . $$What is the expanded form?

Accepted Answer

$$ v^2$ - u^2$ $$

Step-by-Step Guidance for College Algebra: Polynomial Multiplication and Factoring

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