Question

For an each situation, it begin with the square field, measuring X centimetres by X centimetres. The dimensions of this square are to be changed. How do you write an expression for the area of the new square field, and then expand, and simplify? :/

A). The length of a side is being increased by 8 cm.
B). The length is being increased by 12 cm and the width is being decreased by 7 cm.

Answer 1

#A

New side

• X+8

Area

• (x+8)²
• x²+16x+64 cm²

#2

Now it has turned rectangle

Sides

x+12 and x-7

Area

• (x+12)(x-7)

Answer 2

A) (x + 8)² cm² = (x² + 16x + 64) cm²

B) (x + 12)(x + 7) cm² = (x² + 19x + 84) cm²

Explanation:

Formula

Area of a square = s² (where s is the side length)

Given side length of square field:

• x cm

⇒ Area of field = x² cm²

Part A

If the side length of the square field is increased by 8 cm then:

⇒ new side length = (x + 8) cm

Substitute the new side length into the formula for the area of a square:

⇒ Area of field = (x + 8)² cm²

Expand and simplify:

⇒ Area = (x + 8)²

⇒ Area = (x + 8)(x + 8)

⇒ Area = x(x + 8) + 8(x + 8)

⇒ Area = x² + 8x + 8x + 64

⇒ Area = (x² + 16x + 64) cm²

Part B

If the side length of the square field is increased by 12 cm and the width is decreased by 7 cm then:

⇒ new side length a = (x + 12) cm

⇒ new side length b = (x - 7) cm

Substitute the side lengths into the formula for area of a square:

⇒ Area of a square = s × s

⇒ Area of a square = a × b

⇒ Area of the field = (x + 12)(x + 7) cm²

Expand and simplify:

⇒ Area = (x + 12)(x + 7)

⇒ Area = x(x + 7) + 12(x + 7)

⇒ Area = x² + 7x + 12x + 84

⇒ Area = (x² + 19x + 84) cm²