Respuesta :

mhanifa

Answer:

  • 14x + 21

Step-by-step explanation:

Find the difference of areas:

  • A₁ = (x + 5)²
  • A₂ = (x - 2)²
  • A₁ - A₂ = shaded area
  • (x + 5)² - (x - 2)² =
  • x² + 10x + 25 - x² + 4x - 4 =
  • 14x + 21

DᴀʀᴋPᴀʀᴀᴅᴏx

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Area of bigger square : (side)²

  • [tex](x + 5)(x + 5)[/tex]

  • [tex] {x}^{2} + 10x + 25[/tex]

Area of smaller square : (side)²

  • [tex](x - 2)(x - 2)[/tex]

  • [tex] {x}^{2} - 4x + 4[/tex]

Area of shaded region is equal to :

  • Area of bigger square - Area of smaller square

that is :

  • [tex] {x}^{2} + 10x + 25 - ( {x}^{2} - 4x + 4)[/tex]

  • [tex] {x}^{2} + 10x + 25 - {x}^{2} + 4x - 4[/tex]

  • [tex]14x + 21[/tex]

hence, area of shaded region = 14x + 21

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