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

Question

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

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Natalia 1 day 2021-10-14T08:22:48+00:00 1 Answer 0

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    2021-10-14T08:24:03+00:00

    Answer:

    ∗ = 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

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