91Ó°ÊÓ

Polynomial subtraction can seem tricky, but it's straightforward once you get the hang of it. You start by writing down the polynomials you are subtracting. Here, we have:
ewline ewline ewline ewline ewlineewlineewlineewlineewline \( (0.9a^{3} + 0.2a - 5) - (0.7a^{4} - 0.15a - 0.1) \).
ewline When subtracting polynomials, the crucial step is correctly handling the negative sign. This process involves changing the sign of each term in the polynomial we are subtracting.
ewline After distributing the negative sign, our equation now looks like:
ewline +

ewline
• \( 0.9a^{3} + 0.2a - 5 - 0.7a^{4} + 0.15a + 0.1 \)
.
ewline

This is the most significant step since any mistake here could lead to the wrong solution. Make sure to verify the signs of each term once the negative sign has been distributed.

After correctly distributing the negative sign, the next step is to combine like terms. In polynomials, like terms are terms that have the same variables raised to the same power. Here, our expression from the previous step is:
ewline

• \( -0.7a^{4} + 0.9a^{3} + 0.2a + 0.15a - 5 + 0.1 \)
.
ewline

ewline Let's combine the terms that have the same degree of variable \( a \):
ewline

ewline
• \( 0.2a \) and \( 0.15a \)
,

• \( -5 \) and \( 0.1 \)
.
ewline

Combining these, we get:

ewline - \( 0.7a^{4} + 0.9a^{3} + 0.35a - 4.9 \).
ewline

Always double-check that you grouped and combined terms accurately. Combining like terms simplifies the polynomial to its final form.

Distributing negative signs is a key process in polynomial subtraction. This means changing the sign of every term in the polynomial to be subtracted. Take our example:
ewline ewline ewline ewline ewline \( (0.9a^{3} + 0.2a - 5) - (0.7a^{4} - 0.15a - 0.1) \).
ewline By distributing the negative sign, we turn \( - (0.7a^{4} - 0.15a - 0.1) \) into \( -0.7a^{4} + 0.15a + 0.1 \).
ewline ewline ewline This step is vital because any mistake here affects the whole subtraction process. Always take your time with this step, and double-check your work. Properly distributing the negative sign ensures that when you move on to combine like terms, everything will be accurately aligned.