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A square kitchen garden has a side length of (2y+11). Expand the expression for the area of the garden.

Mathematics

ScanSolve AI Answer

Answer

4y2+44y+1214y^2 + 44y + 121

Step-by-step solution

5 steps
  1. Identify the shape and its side length.

    The kitchen garden is in the shape of a square, and each side measures (2y+11)(2y+11).

  2. Write the formula for the area of a square.

    The area AA of a square with side length ss is given by A=s2A = s^2.
    Substitute the given side length:

    A=(2y+11)2A = (2y+11)^2
  3. Apply the quadratic identity (a+b)2=a2+2ab+b2(a+b)^2 = a^2 + 2ab + b^2.

    In this expression, a=2ya = 2y and b=11b = 11.
    Substitute these values into the identity:

    A=(2y)2+2(2y)(11)+(11)2A = (2y)^2 + 2(2y)(11) + (11)^2
  4. Simplify each term.

    (2y)2=4y2(2y)^2 = 4y^2 2(2y)(11)=44y2(2y)(11) = 44y (11)2=121(11)^2 = 121
  5. Combine the simplified terms to get the area.

    A=4y2+44y+121A = 4y^2 + 44y + 121

    The area of the kitchen garden is:

    4y2+44y+1214y^2 + 44y + 121
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