Factoring Polynomials: Differences of Squares Explained

What results from multiplying x by -4 in the expression x(x - 4)?

• -4x

• -16

• 4x

• x^2

What is the factored form of x^2 - 16?

• (x + 4)(x - 4)

• None of the above

• x + 4, x - 4

• x^2(1 - 16)

Which condition is necessary for applying the differences of squares rule?

• Both terms must be multiplied

• Both terms must be perfect squares

• None of the above

• There must be an addition between terms

What is the factored form of 25m^2 - 1?

• Cannot be factored

• 5m^2 - 1

• 25m(m - 1)

• (5m + 1)(5m - 1)

For the expression 4a^2 - 9b^2, what are the square roots of the terms?

• 2a and 3b

• 4a and 9b

• 2a^2 and 3b^2

• None of the above

What is the correct factored form of 4a^2 - 9b^2 using the differences of squares?

• (2a + 3b)(2a - 3b)

• 4a^2 - 9b^2

• 4a(2 - 9b)

• Cannot be factored

What does the square root of 121r^6 simplify to?

• 121r^3

• Cannot be simplified

• 11r^6

• 11r^3

What is the factored form of 121r^6 - 1?

• 121(r^6 - 1)

• 121r^3 - 1

• (11r^3 + 1)(11r^3 - 1)

• Cannot be factored

What is the GCF of 80n^4 and 125n^2?

• 25n^2

• 5n^2

• None of the above

• 5n^4

After factoring out the GCF, what is the factored form of the expression 16n^2 - 25?

• 16n^2 - 25

• 16n(n - 25)

• (4n - 5)(4n + 5)

• Cannot be factored