## Replace ∗ with a monomial so that the derived equality will be an identity: (15y + ∗)2 = 225y2+12x3y+0.16×6

Question

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## Answers ( )

Answer:∗ = 0.4x³Step-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