Thread: Problems I need help with...

1. Problems I need help with...

Problem 1. 4x (3x3 – 5x2)

Problem 2. a3 (2a2 + 6a + 5)

Problem 3. 5y4 – 4y3 – 3y2 + y3 + 3y2 + 2 + 6y – 5

Problem 4. (x2 + 7x + 12) – ( – x3 + 2x2 – x + 1)

Problem 5. 5x3 – 6x2 + x + 3 (x3 – 3x2 – x)

Problem 6. y2 + 3y + 6 + 4 (y2 – 3y – 4)

Problem 7. a3b2 (3a2 – 4ab + 5b2)

Problem 8. – 7xy (x3 + 3x2y – 3xy2 + y3)

Problem 9. mn2 (m2 – 4mn – 6n2) – 4mn2 (6m2 – n2)

Problem 10. (a2 + 3a + 4) + (5a3 – a + 2)

Problem 11. (y4 – 2y2 – y) + ( – 2y3 – y2 – 4y)

Problem 12. Subtract a2 – 4a from 3a3 + 4a2 + a + 3

Problem 13. Subtract – a3 + 2a from a3 + a2 – a + 3

Thank you.

2. Hello, slykksta!

I'll do a few of these for you.
If you really need help of all of these, I suggest you see your teacher/tutor.
You seem to be missing a lot of information!

$1)\;\;4x(3x^3 - 5x^2)$
You're expected to know how to "distribute" terms and simplify.

$(4x)(3x^3) - (4x)(5x^2) \;\;=\;\;12x^4 - 20x^3$

$3)\;\; 5y^4 - 4y^3 - 3y^2 + y^3 + 3y^2 + 2 + 6y - 5$
You're expected to know how to combine "like" terms.

We have: . $5y^4 \,\underbrace{-4y^3 \,+ \,y^3}\, \underbrace{-\,3y^2 + 3y^2}\,+\,6y \,\underbrace{+\,2 - 5}\;\;= \;\;5y^4 -3y^3 + 6y - 3$

$4)\;\;(x^2 + 7x + 12) - ( -x^3 + 2x^2 - x + 1)$
We have: . $x^2 + 7x + 12 + x^3 - 2x^2 + x - 1 \;\;=\;\;x^3 - x^2 + 8x + 11$

$7)\;\;a^3b^2 (3a^2 - 4ab + 5b^2)$

Distribute and use the exponent rules:

. . $(a^3b^2)(3a^2) - (a^3b^2)(4ab) + (a^3b^2)(5b^2) \;\;=\;\;3a^5b^2 - 4a^4b^3 + 5a^3b^4$

$12)\;\;\text{Subtract }a^2 - 4a \text{ from }3a^3 + 4a^2 + a + 3$
We have: . $(3a^3+4a^2+a+3) - (a^2-4a)$

. . $=\;\;3a^3 + 4a^2 + a + 3 - a^2 - 4a \;=\;3a^3 + 3a^2 - 3a + 3$