Answer:
The new area of the smaller rectangle is 16 - x² units²
Explanation:
The dimensions of the small rectangles are 2 + x and 2 - x
∵ The length of the small rectangle is 2 + x units
∵ The length is adding by 2 units
∴ The new length = 2 + x + 2 = 4 + x units
∵ The width of the small rectangle is 2 - x units
∵ The width is adding by 2 units
∴ The new width = 2 - x + 2 = 4 - x units
∵ Area of the rectangle = length × width
∴ The new area of the smaller rectangle = (4 + x) × (4 - x)
→ Simplify it by multiplying the 2 brackets
∵ (4 + x)(4 - x) = (4)(4) + (4)(-x) + (x)(4) + x(-x)
∴ (4 + x)(4 - x) = 16 + (-4x) + 4x + (-x²)
→ Remember (+)(-) = (-)
∴ (4 + x)(4 - x) = 16 - 4x + 4x - x²
→ Add the like terms
∴ (4 + x)(4 - x) = 16 - x²
∴ The new area of the smaller rectangle is 16 - x² units²