Can someone check my math answers?

Question

 

Factor
1)2y^3-50y
2)4n^2+11n-3
3) b^2+3b-40
4)10y^4+50y^3-500y^2

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Answer 1

1) 2y^3-50y

2y is common in both terms

= 2y (y^2 - 25)

= 2y (y^2 - 5^2)

= 2y (y + 5) (y - 5)

Factors of 2y^3-50y is 2y (y + 5) (y - 5)

Answer 2

2) 4n^2+11n-3

11n  can be written as 12n -1n

= 4n^2+12n -n -3

Distributive property ab+ ac = a( b + c )

= 4n(n+3) -1(n+3)

n+3 is common in both terms

= (n+3) (4n -1)

Factor of  4n^2+11n-3 is (n+3) (4n -1)

 

 

Answer 3

3) b^2+3b-40

3b can be written as 8b - 5b

= b^2 + 8b - 5b - 40

Distributive property ab+ ac = a( b + c )

= b (b + 8) - 5 (b + 8)

b + 8 is common in both terms

= ( b + 8 )( b - 5 )

Factor of b^2+3b-40 is ( b + 8 )( b - 5 )

Answer 4

4) 10y^4+50y^3 - 500y^2

50y^3  can be written as 100y^3 - 50y^3

= 10y^4+100y^3 - 50y^3 - 500y^2

Distributive property ab+ ac = a( b + c )

= 10y^3 (y+10) - 50y^2(y+10)

y+10 is common in both terms

= (y+10) (10y^3 -50y^2)

= (y+10) (10y^2) (y -5)

= 10y (y) (y+10) (y -5)

Factor of 10y^4+50y^3-500y^2 is 10y (y) (y+10) (y -5)

Answer 5

10y^4 + 50y^3 - 500y^2

10y^2 is common both terms

=10y^2(y^2 + 5y -50 )

=  10y^2 (y^2 +10y -5y -50 )

Distributive property ab+ ac = a( b + c )

=10y^2 ( y( y+ 10 ) - 5( y+10)

y +10 is common  in both terms

=10y^2( y +10) (y - 5)

=(10y )(y) (y+10) (y -5)

factor of 10y^4 + 50y^3 - 500y^2=(10y )(y) (y+10) (y -5)