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)

= x^{2} + 4x + 4x + 16

= x^{2} + 8x + 16

The area of the inner square of side x cm = x^{2}

Now, area of shaded region = Area of the outer square - area of the inner square

= x^{2} + 8x + 16 - x^{2}

= 8x + 16

Final Answer:

Hence, the area of the shaded region is 8x + 16.

^{2}+ 4x + 4x + 16

^{2}+ 8x + 16

The area of the inner square of side x cm = x

^{2}

Now, area of shaded region = Area of the outer square - area of the inner square

^{2}+ 8x + 16 - x

^{2}

Final Answer:

Hence, the area of the shaded region is 8x + 16.

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