# Multiply (25x^2-4)/(2x^2-11x-21)*(2x-14)/(5x-2) 25×2-42×2-11x-21⋅2x-145x-2
Simplify the numerator.
Rewrite 25×2 as (5x)2.
(5x)2-42×2-11x-21⋅2x-145x-2
Rewrite 4 as 22.
(5x)2-222×2-11x-21⋅2x-145x-2
Since both terms are perfect squares, factor using the difference of squares formula, a2-b2=(a+b)(a-b) where a=5x and b=2.
(5x+2)(5x-2)2×2-11x-21⋅2x-145x-2
(5x+2)(5x-2)2×2-11x-21⋅2x-145x-2
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=2⋅-21=-42 and whose sum is b=-11.
Factor -11 out of -11x.
(5x+2)(5x-2)2×2-11(x)-21⋅2x-145x-2
Rewrite -11 as 3 plus -14
(5x+2)(5x-2)2×2+(3-14)x-21⋅2x-145x-2
Apply the distributive property.
(5x+2)(5x-2)2×2+3x-14x-21⋅2x-145x-2
(5x+2)(5x-2)2×2+3x-14x-21⋅2x-145x-2
Factor out the greatest common factor from each group.
Group the first two terms and the last two terms.
(5x+2)(5x-2)(2×2+3x)-14x-21⋅2x-145x-2
Factor out the greatest common factor (GCF) from each group.
(5x+2)(5x-2)x(2x+3)-7(2x+3)⋅2x-145x-2
(5x+2)(5x-2)x(2x+3)-7(2x+3)⋅2x-145x-2
Factor the polynomial by factoring out the greatest common factor, 2x+3.
(5x+2)(5x-2)(2x+3)(x-7)⋅2x-145x-2
(5x+2)(5x-2)(2x+3)(x-7)⋅2x-145x-2
Factor 2 out of 2x-14.
Factor 2 out of 2x.
(5x+2)(5x-2)(2x+3)(x-7)⋅2(x)-145x-2
Factor 2 out of -14.
(5x+2)(5x-2)(2x+3)(x-7)⋅2x+2⋅-75x-2
Factor 2 out of 2x+2⋅-7.
(5x+2)(5x-2)(2x+3)(x-7)⋅2(x-7)5x-2
(5x+2)(5x-2)(2x+3)(x-7)⋅2(x-7)5x-2
Cancel the common factor of 5x-2.
Factor 5x-2 out of (5x+2)(5x-2).
(5x-2)(5x+2)(2x+3)(x-7)⋅2(x-7)5x-2
Cancel the common factor.
(5x-2)(5x+2)(2x+3)(x-7)⋅2(x-7)5x-2
Rewrite the expression.
5x+2(2x+3)(x-7)⋅(2(x-7))
5x+2(2x+3)(x-7)⋅(2(x-7))
Cancel the common factor of x-7.
Factor x-7 out of (2x+3)(x-7).
5x+2(x-7)(2x+3)⋅(2(x-7))
Factor x-7 out of 2(x-7).
5x+2(x-7)(2x+3)⋅((x-7)⋅2)
Cancel the common factor.
5x+2(x-7)(2x+3)⋅((x-7)⋅2)
Rewrite the expression.
5x+22x+3⋅2
5x+22x+3⋅2
Combine 5x+22x+3 and 2.
(5x+2)⋅22x+3
Move 2 to the left of 5x+2.
2(5x+2)2x+3
Multiply (25x^2-4)/(2x^2-11x-21)*(2x-14)/(5x-2)

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