Simplify (x-7/5)(x+5/7)

Math
(x-75)(x+57)
Expand (x-75)(x+57) using the FOIL Method.
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Apply the distributive property.
x(x+57)-75(x+57)
Apply the distributive property.
x⋅x+x57-75(x+57)
Apply the distributive property.
x⋅x+x57-75x-75⋅57
x⋅x+x57-75x-75⋅57
Simplify and combine like terms.
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Simplify each term.
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Multiply x by x.
x2+x57-75x-75⋅57
Combine x and 57.
x2+x⋅57-75x-75⋅57
Move 5 to the left of x.
x2+5⋅x7-75x-75⋅57
Combine x and 75.
x2+5×7-x⋅75-75⋅57
Move 7 to the left of x.
x2+5×7-7⋅x5-75⋅57
Cancel the common factor of 7.
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Move the leading negative in -75 into the numerator.
x2+5×7-7×5+-75⋅57
Factor 7 out of -7.
x2+5×7-7×5+7(-1)5⋅57
Cancel the common factor.
x2+5×7-7×5+7⋅-15⋅57
Rewrite the expression.
x2+5×7-7×5+-15⋅5
x2+5×7-7×5+-15⋅5
Cancel the common factor of 5.
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Cancel the common factor.
x2+5×7-7×5+-15⋅5
Rewrite the expression.
x2+5×7-7×5-1
x2+5×7-7×5-1
x2+5×7-7×5-1
To write 5×7 as a fraction with a common denominator, multiply by 55.
x2+5×7⋅55-7×5-1
To write -7×5 as a fraction with a common denominator, multiply by 77.
x2+5×7⋅55-7×5⋅77-1
Write each expression with a common denominator of 35, by multiplying each by an appropriate factor of 1.
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Multiply 5×7 and 55.
x2+5x⋅57⋅5-7×5⋅77-1
Multiply 7 by 5.
x2+5x⋅535-7×5⋅77-1
Multiply 7×5 and 77.
x2+5x⋅535-7x⋅75⋅7-1
Multiply 5 by 7.
x2+5x⋅535-7x⋅735-1
x2+5x⋅535-7x⋅735-1
Combine the numerators over the common denominator.
x2+5x⋅5-7x⋅735-1
To write x2 as a fraction with a common denominator, multiply by 3535.
x2⋅3535+5x⋅5-7x⋅735-1
Combine x2 and 3535.
x2⋅3535+5x⋅5-7x⋅735-1
Combine the numerators over the common denominator.
x2⋅35+5x⋅5-7x⋅735-1
To write -1 as a fraction with a common denominator, multiply by 3535.
x2⋅35+5x⋅5-7x⋅735-1⋅3535
Combine -1 and 3535.
x2⋅35+5x⋅5-7x⋅735+-1⋅3535
Combine the numerators over the common denominator.
x2⋅35+5x⋅5-7x⋅7-1⋅3535
x2⋅35+5x⋅5-7x⋅7-1⋅3535
Simplify the numerator.
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Move 35 to the left of x2.
35⋅x2+5x⋅5-7x⋅7-1⋅3535
Multiply 5 by 5.
35×2+25x-7x⋅7-1⋅3535
Multiply 7 by -7.
35×2+25x-49x-1⋅3535
Multiply -1 by 35.
35×2+25x-49x-3535
Subtract 49x from 25x.
35×2-24x-3535
Factor by grouping.
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For a polynomial of the form ax2+bx+c, rewrite the middle term as a sum of two terms whose product is a⋅c=35⋅-35=-1225 and whose sum is b=-24.
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Factor -24 out of -24x.
35×2-24(x)-3535
Rewrite -24 as 25 plus -49
35×2+(25-49)x-3535
Apply the distributive property.
35×2+25x-49x-3535
35×2+25x-49x-3535
Factor out the greatest common factor from each group.
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Group the first two terms and the last two terms.
(35×2+25x)-49x-3535
Factor out the greatest common factor (GCF) from each group.
5x(7x+5)-7(7x+5)35
5x(7x+5)-7(7x+5)35
Factor the polynomial by factoring out the greatest common factor, 7x+5.
(7x+5)(5x-7)35
(7x+5)(5x-7)35
(7x+5)(5x-7)35
Simplify (x-7/5)(x+5/7)

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