Factor z^2+8zy+15y^2

Math
z2+8zy+15y2
For a polynomial of the form ax2+bx+c, rewrite the middle term as a sum of two terms whose product is a⋅c=15⋅1=15 and whose sum is b=8.
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Reorder terms.
15y2+z2+8yz
Reorder z2 and 8yz.
15y2+8yz+z2
Factor 8 out of 8yz.
15y2+8(yz)+z2
Rewrite 8 as 3 plus 5
15y2+(3+5)(yz)+z2
Apply the distributive property.
15y2+3(yz)+5(yz)+z2
Remove unnecessary parentheses.
15y2+3yz+5(yz)+z2
Remove unnecessary parentheses.
15y2+3yz+5yz+z2
15y2+3yz+5yz+z2
Factor out the greatest common factor from each group.
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Group the first two terms and the last two terms.
(15y2+3yz)+5yz+z2
Factor out the greatest common factor (GCF) from each group.
3y(5y+z)+z(5y+z)
3y(5y+z)+z(5y+z)
Factor the polynomial by factoring out the greatest common factor, 5y+z.
(5y+z)(3y+z)
Factor z^2+8zy+15y^2

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