Chapter R – Part 1 Day 4 Notes (Algebra II)

Flashcards covering special products, multiplying conjugates, division (monomial and binomial), and degree rules for polynomials from the Day 4 notes.

Expand (2x + 3)^2.

4x^2 + 12x + 9

Expand (3x − 5)^2.

9x^2 − 30x + 25

Expand (7x + 4)^2.

49x^2 + 56x + 16

What is the product of conjugates (a + b)(a − b)?

a^2 − b^2

Compute (3x + 8)(3x − 8).

9x^2 − 64

Expand (2a + 5)(2a + 3).

4a^2 + 16a + 15

Expand (qp − 5pq)^2.

16 p^2 q^2 (since qp = pq) or (-4pq)^2 = 16p^2q^2.

Expand (3yx − 2xy)^2.

x^2 y^2

Divide the polynomial (18xy^2 − 24xy) by the monomial 6xy.

3y − 4

Divide 2x^3 − 3x^2 + x by (x − 1).

2x^2 − x

If deg(F) = m and deg(G) = n with n < m, what is the maximum possible degree of F + G?

At most m (could be m if the leading terms do not cancel).

What is the degree of F − G when deg(F) = m and deg(G) = n with n < m?

At most m (could be less if cancellation occurs).

What is the degree of the product F · G when deg(F) = m and deg(G) = n with n < m?

m + n

What is the degree of (F)^2 if deg(F) = m?

2m