math destroyer test 1 #10

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ysurge19

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question presents a circle in a circle (two circle sharing a common center). The inner circle radius = x inches. outer circle width = 6 inches. Find the expression that represents the area of the walkway in square inches.

  • (area of inner circle + area of outer circle) - (area of inner circle) = area of outer circle
  • (the area of the inner circle + area of outer circle) = (pi)(x+6)^2
  • (the area of inner circle) = (pi)(x^2)

  • Book solution states that the (area of inner + outer) = (pi)(x+6)^2 = pi(x^2 + 12x +36) ???
  • pi(x^2 + 12x +36) - (pi)(x^2) = pi(12x +36) = (12pi)(x+3) ???
Can someone show me how they got this? Confused on the algebra. Thanks!