(x-75)(x+57)

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 each term.

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.

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.

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.

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

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.

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.

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.

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)