Write (98 - 0.18x) times 270 squared in expanded form.

Step-by-step solution

1. 1

   Square the constant first. $270=27\cdot 10$, so

   $270^2=27^2\cdot 10^2=729\cdot 100=72900$

   Pulling the powers of ten out avoids a long multiplication.

2. 2

   Restate as a binomial times a constant.

   $(98-0.18x)\cdot 270^2=(98-0.18x)\cdot 72900$

   Only one distribution is left to do.

3. 3

   Distribute, keeping the sign with its term.

   $=98\cdot 72900-0.18x\cdot 72900$

4. 4

   Compute the constant term. Use $98=100-2$:

   $98\cdot 72900=7290000-145800=7144200$

5. 5

   Compute the $x$ coefficient — it comes out whole.

   $0.18\cdot 72900=\frac{18\cdot 72900}{100}=\frac{1312200}{100}=13122$

   Because $72900$ is divisible by $100$, the decimal disappears entirely, so the expansion is $7144200-13122x$ with integer coefficients.

6. 6

   Verify at $x=50$. Original: $(98-9)\cdot 72900=89\cdot 72900=6488100$. Expansion: $7144200-13122\cdot 50=7144200-656100=6488100$. The two agree, confirming the result.