Replace ∗ with a monomial so that the derived equality will be an identity: (15y + ∗)2 = 225y2+12x3y+0.16x6

∗ = 0.4x³

Step-by-step explanation:

(15y + ∗)² = 225y²+12x³y+0.16x⁶

Note:

225y² = 15y * 15y = (15y)²

12x³y = 2 * 15y * 0.4x³

0.16x⁶ = 0.4x³ * 0.4x³ = (0.4x³)²

So, by factoring the right hand side:

225y²+12x³y+0.16x⁶ = (15y + 0.4x³)²

By comparing the left hand side with (15y + 0.4x³)²

So, ∗ should be replaced with the monomial 0.4x³