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

Step-by-step solution

1. 1

   Collapse the numeric square before touching the bracket. The factor $98^2$ contains no variable, so it is just a number and can be evaluated once and for all:

   $98^2=(100-2)^2=10000-400+4=9604$

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

2. 2

   Rewrite the problem as one product.

   $(515-0.27x)\cdot 98^2=(515-0.27x)\cdot 9604$

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

3. 3

   Distribute across the subtraction.

   $(515-0.27x)\cdot 9604=515\cdot 9604-0.27x\cdot 9604$

   The minus sign stays attached to the second term; both terms get the full factor $9604$.

4. 4

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

   $515\cdot 9604=500\cdot 9604+15\cdot 9604=4802000+144060=4946060$

   and for the coefficient of $x$,

   $0.27\cdot 9604=2593.08$

   so the expanded form is $4946060-2593.08x$.

5. 5

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