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Question 557355: I need help with this problem please (sqrtx+7)(sgrtx-7)=?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! (sqrt(x) + 7) * (sqrt(x) - 7) is solved using the distributive law of algebraic operations as follows:
(sqrt(x) + 7) * (sqrt(x) - 7) is equal to:
(sqrt(x) * (sqrt(x) - 7)) + 7 * (sqrt(x) - 7) which becomes:
sqrt(x) * sqrt(x) - 7 * sqrt(x) + 7 * sqrt(x) - 49
combine like terms to get:
sqrt(x) * sqrt(x) - 49 which becomes:
(sqrt(x))^2 - 49 which becomes:
x - 49
this is because sqrt(x) * sqrt(x) is equal to (sqrt(x))^2 is equal to x.
this might be seen clearer if you use exponent arithmetic.
sqrt(x) is equal to x^(1/2)
sqrt(x) * sqrt(x) is therefore equal to:
x^(1/2) * x^(1/2)
by the laws of exponent arithmetic, this becomes:
x^((1/2) + (1/2)) which becomes x^1 which becomes x.
the whole thing might be easier to see if you allow:
y = sqrt(x).
your equation of:
(sqrt(x)+7) * (sqrt(x)-7) becomes:
(y+7)*(y-7)
you can use foil or you can use the distributive property of arithmetic (foil is just a subset of the distributive property) to get:
y^2 - 7y + 7y - 49
the -7y and the + 7y cancel out and you are left with:
y^2 - 49
since y = sqrt(x), then y^2 = x and you are left with:
x - 49.
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