 # Pt1420 Unit 2 Study Guide

Good Essays
Chase Williams
Ms. Haramis
Complete the following exercises by applying polynomial identities to complex numbers.
1. Factor x2 + 64. Check your work.
2. Factor 16x2 + 49. Check your work.
3. Find the product of (x + 9i)2.
4. Find the product of (x − 2i)2.
5. Find the product of (x + (3+5i))2.
1. x^2 +64=
2. 16x^2+49=
3. (x+9i)^2= (x+9i)(x+9i= x^2+9ix+9ix+81i^2=x^2+18ix+(-81)=
4. (x-2i)^2=(x-2i)(x-2i)=x^2-2ix-2ix+4i^2=x^2-4ix+(-4)=
5. (x+(3+5i))^2=(x+(3+5i)(x+(3+5i)
X^2+3x+5ix+3x+9+15i+5ix+15i+25i^2=x^2+6x+10ix+30i+25i^2+9=

Expand the following using the Binomial Theorem and
(x + 2)6
2. (x − 4)4
3. (2x + 3)5
4. (2x − 3y)4
5. In the expansion of (3a + 4b)8, which of the following are possible variable terms? Explain your reasoning. a2b3; a5b3; ab8; b8; a4b4; a8; ab7; a6b5
1. (x +
(2x − 3y)^4=16x^4-96x^3y+216x^2y^2-216xy3+81y^4
5. The possible variable terms would have to be a2b3; a5b3; ab8; b8; a4b4; a8; ab7; a6b5 because the exponents of each one of the terms all add up to 8.