To subtract the given polynomials [tex]\((7x^2 + 10x + 3) - (-18x + 5)\)[/tex], follow these steps:
1. Rewrite the subtraction as addition by distributing the negative sign through the second polynomial:
[tex]\[
7x^2 + 10x + 3 - (-18x + 5) \quad \text{becomes} \quad 7x^2 + 10x + 3 + (-1)(-18x + 5).
\][/tex]
Distribute the [tex]\(-1\)[/tex]:
[tex]\[
7x^2 + 10x + 3 + 18x - 5.
\][/tex]
2. Combine like terms (terms that have the same power of [tex]\(x\)[/tex]):
- For the [tex]\(x^2\)[/tex] terms: [tex]\(7x^2\)[/tex] (no other [tex]\(x^2\)[/tex] term to combine with).
- For the [tex]\(x\)[/tex] terms: [tex]\(10x + 18x = 28x\)[/tex].
- For the constant terms: [tex]\(3 - 5 = -2\)[/tex].
Therefore, combining these, we get:
[tex]\[
7x^2 + 28x - 2
\][/tex]
So, the resultant polynomial after subtracting [tex]\((-18x + 5)\)[/tex] from [tex]\((7x^2 + 10x + 3)\)[/tex] is:
[tex]\[
7x^2 + 28x - 2
\][/tex]
