Answer:
30) 25x^2 +28x +16
31) (15/2)x +15
32) 18x^3 -21x^2 -52x -20
Step-by-step explanation:
For a shape with a cutout, the shaded area is the difference between the area of the enclosing shape and the area of the cutout. The applicable area formulas are ...
area of rectangle: A = bh
area of triangle: A = (1/2)bh
Here, the dimensions are given as binomials (2-term polynomials), so you have to multiply those to find the areas. The distributive property is helpful for that.
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30) shaded area = (5x+8)(6x+2) -(5x)(x+6)
= (5x)(6x+2) +8(6x+2) -5x^2 -30x
= 30x^2 +10x +48x +16 -5x^2 -30x
shaded area = 25x^2 +28x +16
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31) shaded area = (1/2)(x+6)(2x+5) -x(x+1)
= (1/2)(x(2x+5) +6(2x+5)) -x^2 -x
= (1/2)(2x^2 +5x +12x +30) -x^2 -x
= x^2 +(17/2)x +15 -x^2 -x
shaded area = (15/2)x +15
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32) volume = lwh = (2x -5)(3x +2)(3x +2)
= (2x -5)(3x(3x +2) +2(3x +2))
= (2x -5)(9x^2 +6x +6x +4)
= (2x -5)(9x^2 +12x +4)
= 2x(9x^2 +12x +4) -5(9x^2 +12x +4)
= 18x^3 +24x^2 +8x -45x^2 -60x -20
volume = 18x^3 -21x^2 -52x -20
