Question
What is the area of the shaded region?
Hint:
The methods used to find the product of binomials are called special products.
Multiplying a number by itself is often called squaring.
For example (x + 3)(x + 3) = (x + 3)2
Area of a square = (side)2
The correct answer is: 8x + 16.
The area of the outer square of side x+4 units = (x+4)2
(x+4)2 = (x+4)(x+4) = x(x+4) +4(x+4)
= x(x) + x(4) +4(x) +4(4)
= x2 + 4x + 4x + 16
= x2 + 8x + 16
The area of the inner square of side x cm = x2
Now, area of shaded region = Area of the outer square - area of the inner square
= x2 + 8x + 16 - x2
= 8x + 16
Final Answer:
Hence, the area of the shaded region is 8x + 16.
The area of the inner square of side x cm = x2
Now, area of shaded region = Area of the outer square - area of the inner square
Final Answer:
Hence, the area of the shaded region is 8x + 16.
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