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Algebra · real student question

Write (515 - 0.27x) times 98 squared in expanded form.

Question

Expand:

(515−0.27x)⋅982(515-0.27x)\cdot 98^2

Step-by-step solution

  1. Collapse the numeric square before touching the bracket. The factor 98298^2 contains no variable, so it is just a number and can be evaluated once and for all:

    982=(100−2)2=10000−400+4=960498^2=(100-2)^2=10000-400+4=9604

    Doing this first keeps the distribution to one multiplication per term instead of two.

  2. Rewrite the problem as one product.

    (515−0.27x)⋅982=(515−0.27x)⋅9604(515-0.27x)\cdot 98^2=(515-0.27x)\cdot 9604

    The expression is now a binomial times a single constant — the standard shape for the distributive law.

  3. Distribute across the subtraction.

    (515−0.27x)⋅9604=515⋅9604−0.27x⋅9604(515-0.27x)\cdot 9604=515\cdot 9604-0.27x\cdot 9604

    The minus sign stays attached to the second term; both terms get the full factor 96049604.

  4. Do the two multiplications. Split the first one to keep it mental:

    515⋅9604=500⋅9604+15⋅9604=4802000+144060=4946060515\cdot 9604=500\cdot 9604+15\cdot 9604=4802000+144060=4946060

    and for the coefficient of xx,

    0.27⋅9604=2593.080.27\cdot 9604=2593.08

    so the expanded form is 4946060−2593.08x4946060-2593.08x.

  5. Check at two values of xx. At x=0x=0 the original is 515⋅9604=4946060515\cdot 9604=4946060, matching the constant term. At x=100x=100 the original is (515−27)⋅9604=488⋅9604=4686752(515-27)\cdot 9604=488\cdot 9604=4686752, and the expansion gives 4946060−259308=46867524946060-259308=4686752. Two independent agreements confirm both coefficients.

Answer

(515−0.27x)⋅982=4946060−2593.08x(515-0.27x)\cdot 98^2=4946060-2593.08x

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