Question

•Find the product using suitable identity : (3y + 5z) (9y2 – 15yz + 25z2 ) ​

Answer 1

Answer:

$(3y + 5z) (9y^2-15yz + 25z^2 ) = 27y^3+125z^3-75yz^2-45zy^2$

Step-by-step explanation:

$(3y + 5z) (9y^2-15yz + 25z^2 ) \\ \\ (3y+5z)[(3y)^2-2\cdot3y\cdot5z+(5z)^2]\\ \\ (3y+5z)(3y-5z)^2\\ \\ (3y+5z)(3y-5z)(3y-5z)$

$[(3y)^2-(5z)^2](3y-5z)$

We know that,

                     $(a-b)(a^2-b^2)=a^3-ab^2+b^3-ba^2$

so,

                           $[(3y)^2-(5z)^2](3y-5z)\\ \\ (3y)^3+(5z)^3-(3y)(5z)^2-5z(3y)^2\\ \\ 27y^3+125z^3-75yz^2-45zy^2$