Factor by Grouping (5x-22)(x+40)

Math
(5x-22)(x+40)
Expand (5x-22)(x+40) using the FOIL Method.
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Apply the distributive property.
5x(x+40)-22(x+40)
Apply the distributive property.
5x⋅x+5x⋅40-22(x+40)
Apply the distributive property.
5x⋅x+5x⋅40-22x-22⋅40
5x⋅x+5x⋅40-22x-22⋅40
Simplify and combine like terms.
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Simplify each term.
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Multiply x by x by adding the exponents.
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Move x.
5(x⋅x)+5x⋅40-22x-22⋅40
Multiply x by x.
5×2+5x⋅40-22x-22⋅40
5×2+5x⋅40-22x-22⋅40
Multiply 40 by 5.
5×2+200x-22x-22⋅40
Multiply -22 by 40.
5×2+200x-22x-880
5×2+200x-22x-880
Subtract 22x from 200x.
5×2+178x-880
5×2+178x-880
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=5⋅-880=-4400 and whose sum is b=178.
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Factor 178 out of 178x.
5×2+178(x)-880
Rewrite 178 as -22 plus 200
5×2+(-22+200)x-880
Apply the distributive property.
5×2-22x+200x-880
5×2-22x+200x-880
Factor out the greatest common factor from each group.
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Group the first two terms and the last two terms.
(5×2-22x)+200x-880
Factor out the greatest common factor (GCF) from each group.
x(5x-22)+40(5x-22)
x(5x-22)+40(5x-22)
Factor the polynomial by factoring out the greatest common factor, 5x-22.
(5x-22)(x+40)
(5x-22)(x+40)
Factor by Grouping (5x-22)(x+40)

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