Multiplying Polynomials

Here you will find a concise collection of multiplying polynomials practice problems. Visit this page directly at hunkim.com/multiply

1. Expand and simplify the following polynomials:
   1. -3x(x-1)
      Solution
      =-3x^2+3x
   2. 2x^2(2-3x+4x^2)
      Solution
      =8x^4-6x^3+4x^2
   3. -(2-3x^2+2x^5-3x)
      Solution
      =-2x^5+3x^2+3x-2
   4. (x-3)(x-5)
      Solution
      =x^2-8x+15
   5. (3x-2)(x-3)
      Solution
      =3x^2-11x+6
   6. (2x-7)^2
      Solution
      =4x^2-28x+49
   7. 2(3x-1)^2
      Solution
      =18x^2-12x+2
   8. 2(3x-1)(x-2)
      Solution
      =6x^2-14x+4
   9. (x+2)(-2)(x-4)
      Solution
      =-2x^2+4x+16
   10. (x-1)(x^2+x+1)
       Solution
       =x^3-1
   11. (x^2-x-2)(x+1)
       Solution
       =x^3-3x-2
   12. (x^2+x+1)(1-x-x^2)
       Solution
       =-x^4-2x^3-x^2+1
   13. (x-1)^4
       Solution
       =x^4-4x^3+6x^2-4x+1
2. Represent the product of (2x-1)(x+2) using algebra tiles.
   Solution
   
   
3. The length of an edge of a cube is x-1
   1. Find the volume of the cube in expanded form
      Solution
      =x^3-3x^2+3x-1
   2. Find the area of the cube
      Solution
      6x^2-12x+6
4. Area of the shaded region below?
   
   Solution
   =2x^2+14x+30
5. See ramp below:
   
   1. Volume?
      Solution
      =260x
   2. Area including the bottom?
      Solution
      c=\sqrt{116}=2\sqrt{29}
      A=\left(180+20\sqrt{29}\right) x+52
6. The diameter of a circle is 2x+4
   1. Area in expanded form?
      Solution
      =\pi x^2+4\pi x+4\pi
   2. Circumference?
      Solution
      \pi(2x+4)=2\pi x+4\pi
7. The area of the top of a cylinder is 9\pi m² and the height is 10x. Find the lateral area of the cylinder.
   Solution
   =60\pi x m²
8. The volume of a square-based pyramid is 3.\bar{3} m³.  Find the volume of a box that has the same height and base.
   Solution
   10
9. The volume of a cylinder is 120\pi x cm³.  Find the volume of a cone that has the same height and base.
   Solution
   40\pi x cm³
10. Challenge:
    1. The diameter of earth is about 12.742x km.  Earth has a volume of about 1,083, 206, 916, 846 km³.
       1. Given the volume of a sphere is V=\frac{4}{3}\pi r^3, find x
          Solution
          1000
       2. Now estimate the surface area of earth given the area of a sphere is A=4\pi r^2
          Solution
          \approx 510,064,479.9 km²
    2. The surface area of the side of a cone is A=\pi rs. s is the length of the diagonal slant of the cone.  Given the diameter of the cone’s base is 6 and the height of the cone is 4x, find the entire area of the cone including the base.
       Solution
       =3\pi \sqrt{16x^2+9}
    3. A swimming pool can barely fit four unit circles on its base (each circle has a radius of 1 unit).  Given the depth of the pool is x, find the surface area of the pool liner that must cover the base and sides of the pool.  See top view of the pool below:
       
       Solution
       2\pi x+\pi +12=(2x+1)\pi+12

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