Question

Mr jones has a square that measures 10 feet on each side. He decides to expand the garden by expanding each day by x. Find the expression in standard form thay represents the area of the new expanded garden.

the expression in standard form that represents the area of the new expanded garden is_______. ​

Answer 1

Key Concepts

Area of a Rectangle

Formula:
`A=lw` where l is the length and w is the width

Whenever we modify any of the side lengths, as in make them longer or shorter, we simply add or subtract from l or w.

Standard Form

When a quadratic equation is organized in standard form, it follows the following format:

`y=ax^2+bx+c` where a, b and c are numbers

In standard form, all the terms have been simplified and there are no parentheses to expand.

Solving the Question

We're given:

• Square garden has measurements of 10 ft by 10 ft
• We're expanding each side by x
• We must find the area of the garden in standard form

If we're expanding each side by x, we're simply adding x to each side length:

10 ft by 10 ft ⇒ (x + 10) ft by (x + 10) ft

Now to find the area, we can use the area formula:

`A=(x+10)(x+10)`

This expression can be simplified as l = w:

`A=(x+10)^2`

Putting it into standard form:

We can do this by expanding the parentheses:

`A=(x+10)^2`

⇒ Because this is a perfect square, we can use the following rule to help us expand this equation:

• 
  `(a+b)^2=a^2+2ab+b^2`

`A=x^2+20x+100`

Answer

Therefore, the expression in standard form that represents the area of the new expanded garden is
`x^2+20x+100`.