To subtract the given polynomials, [tex]\(\left(-6.7 x^2 + 2.3 x y + 5.2\right)\)[/tex] and [tex]\(\left(-14.9 x^2 - 3.5 x y + 7.1\right)\)[/tex], follow these detailed steps:
1. Write down the given polynomials:
[tex]\[ -6.7 x^2 + 2.3 x y + 5.2 \][/tex]
[tex]\[ -14.9 x^2 - 3.5 x y + 7.1 \][/tex]
2. Subtract the coefficients of corresponding terms from each polynomial:
- For [tex]\(x^2\)[/tex] terms:
[tex]\[ -6.7 - (-14.9) \][/tex]
This is equivalent to adding 14.9 to -6.7:
[tex]\[ -6.7 + 14.9 = 8.2 \][/tex]
- For [tex]\(xy\)[/tex] terms:
[tex]\[ 2.3 - (-3.5) \][/tex]
This is equivalent to adding 3.5 to 2.3:
[tex]\[ 2.3 + 3.5 = 5.8 \][/tex]
- For the constant terms:
[tex]\[ 5.2 - 7.1 \][/tex]
Subtract 7.1 from 5.2:
[tex]\[ 5.2 - 7.1 = -1.9 \][/tex]
3. Combine the results to form the answer in descending powers of [tex]\(x\)[/tex]:
[tex]\[ 8.2x^2 + 5.8xy - 1.9 \][/tex]
This is the polynomial resulting from the subtraction, written in descending powers of [tex]\(x\)[/tex].
So, the final answer you should place in the grid is:
[tex]\[ \boxed{8.2 x^2 + 5.8 x y - 1.9} \][/tex]
