Generate an inviting, education-themed image containing no text. Illustrate a visual representation of mathematical concepts like algebraic expressions, distributive property, cylinders, surface area, and polynomials. Maintain an element of neutral academic intrigue in the picture, hinting at problem-solving, calculation and mathematical analysis without referencing to any specific questions or solutions. To help set an analytical mood, incorporate abstract representations of algebraic symbols and geometric figures.

1) what is the simplified form of (x-2)(2x+3)? Use the distributive property.

A) 2x^2-x-6
B) 2x^2-6
C)2x^2-7x-6
D) 2x^2 +x-6****

2) what is the simplified form of (3x+2)(4x-3) use a table.
A)12x^2+18x+6
B) 12x^2+x-6
C) 12x^2+18x-6****
D)12x^2-x-6

3) what is the simplified form of (4p-2)(p-4)
A)4p^2+6p-16
B)4p^2-18p+8
C)4p^2-14p-6
D)4p^2-6p+16****

4) the radius of a cylinder is 3x-2 cm. the height of a cylinder is x+3 cm. what is the surface area of the cylinder? Use the formula A=2pi r^2+2pi rh
A) 2pi(3x^2+10x-8)
B) 2pi(12x^2+7x-2)
C) 2pi(12x^2-2x+13)
D) 2pi(12x^2-5x-2)
Pi=the pi symbol I didn't know how to do that

5) what is the simplified form of (2x^2+4x-3)(3x+1)
A) 6x^3+10x^2-5x+5
B) 6x^3+14x+5x-3
C) 6x^3+14x^2-5x-3
D) 6x^3-10x^2-5x-3

A

D
B
D
C

#1, your middle term is -x , thus A

#2 D

#3 B
How are you doing these, so far they are all wrong
(4p-2)(p-4)
= 4p^2 - 16p - 2p + 8
= 4p^2 - 18p + 8

#4
A = 2πr^2 + 2πrh
= 2π(3x-2)^2 + 2π(3x-2)(x+3)
= 2π[ 9x^2 - 6x - 6x + 4 + 3x^2 + 9x - 2x - 6]
= 2π[12x^2 - 5x - 2] ,
which is D

#5
(2x^2+4x-3)(3x+1)
= 6x^3 + 2x^2 + 12x^2 + 4x - 9x - 3
= 6x^3 + 14x^2 - 5x - 3

I think you will need more practise with these.

A

D
B
D
C
D

Algebra 1 B | Unit 3: Polynomials and Factoring

Lesson 3: Multiplying Binomials
---
1. A, 2x^2 - x - 6
2. D, 12x^2 - x - 6
3. B, 4p^2 - 18p + 8
4. D, 2pi(12x^2 - 5x - 2)
5. C, 6x^3 + 14x^2 - 5x - 3

@Meh is correct

Thank you so much, and I know I have been practicing then I jut for some reason don't undertsand

Connections academy

A
D
B
D
C

meh is 100% correct thanks

A

D
B
D
C

MehIsCorrect