Question

Working with Polynomials
1. Multiply and simplify.

2. Simplify and leave answers in STANDARD FORM
answers will be below

Answer 1

1) \[3x ^{2}y ^{8}\times7x ^{4}y ^{-4}\]

Answer 2

So what is the property of exponents when you are multiplying exponential terms with like bases

Answer 3

2)
part A \[(9x ^{2}+8x-5)-(7x ^{2}+2x-2)\]
part B \[2y(2y+3y ^{2})-y ^{2}(3-y)\]

Answer 4

Well let's do number one for now
What is the rule of exponents when multiplying

Answer 5

I'm not sure @Brill

Answer 6

\[\huge 3x ^{2}y ^{8}\times7x ^{4}y ^{-4}\]

that is just a bunch of multiplication of everything together.

the numbers can combine, and the like bases can combine, powers of each variable...

Answer 7

recall ,

x^a * x^b = x^(a + b)

you add exponents like that , when two terms are multiplied

Answer 8

\[\huge 21 * x^{2+4} * y^{8-4}\]

Answer 9

21*x^6*y^4

Answer 10

so it'll be \[21^{6}\times y ^{4} \]

Answer 11

write that exponent rule down,

for this one

\[\large (9x ^{2}+8x-5)-(7x ^{2}+2x-2)\]

all those terms are being added together, the only thing to change, is since the second parenthesis is - , you have to distribute that -1 into it, changes all the signs around

Answer 12

\[\large 9x ^{2}+8x-5 - 7x ^{2} - 2x +2\]

Answer 13

then combine like terms, the x^2, the x, and the numbers can each combine

Answer 14

like this\[2x ^{2}+6x-7?\]

Answer 15

yeah you got it, cept -5 + 2 is -3 on the end

Answer 16

Thank you so much for your help

Answer 17

this one uses that same rule for adding powers from before, first distribute and expand out those parenthesis terms

\[\huge 2y(2y+3y ^{2})-y ^{2}(3-y)\]

\[\huge 4y^2+6y ^{3} -3y ^{2}+y^3\]

Answer 18

then just put together the same powers like before