Question

using the identity (x+a)(x+b),find the product of (3y^2+9)(3y^2-5)

Answer 1

$\huge\bold{\gray{\sf{Answer:}}}$

$\bold{Explanation:}$

Given:

$\sf (3 {y}^{2} + 9)(3 {y}^{2} - 5)$

To Find :

Product

Above equation is in the form of (x+a)(x-b)

So,here we use this identity:

$\bold{\boxed{(x + a)(x - b) = {x}^{2} - (a + b)x + ab}}$

X is 3y^2 ,a=9 and b=5

$\sf (3 {y}^{2} + 9)(3 {y}^{2} - 5) = {(3 {y}^{2} )}^{2} - (9 + 5)x + 9 \times 5$

$\sf = 9 {y}^{4} - 14x + 45$

Other Identities:

• $\bold{\boxed{ {(x -y)}^{2} = {x}^{2} + {y}^{2} - 2xy}}$
• $\bold{\boxed{ {x}^{3} + {y}^{3} = {x}^{3} + {y}^{3} + 3xy(x + y)}}$
• $\bold{\boxed{(x + a)(x + b) = {x}^{2} + (a+ b)x + ab}}$
• $\bold{\boxed{ {(x +y)}^{3} = {x}^{3} + {y}^{3} +3xy[x+y]}}$

• $\bold{\boxed{(x + a)(x - b) = {x}^{2} + (a - b)x - ab}}$
• $\bold{\boxed{(x - a)(x - b) = {x}^{2} - (a + b)x + ab}}$