Answer:
shaded area = x^2 -3x +36
Step-by-step explanation:
The area of the shaded region is the overall area less the area of the unshaded enclosed rectangle. The area of a rectangle is the product of its length and width, so the shaded area is ...
shaded area = (x +1)(x +1) -(x -7)(5)
= (x^2 +2x +1) -(5x -35)
= x^2 +2x +1 -5x +35
shaded area = x^2 -3x +36
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Additional comment
You can find the product of two binomials using the distributive property:
(x +1)(x +1) = x(x +1) +1(x +1)
= (x^2 +x) +(x +1) = x^2 +2x +1
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Or, in this case, you can take advantage of the form for the square of a binomial:
(x +a)^2 = x^2 +2ax +a^2
For a=1, this is ...
x^2 +2x +1
