Question

In your notebook, set up the following subtraction in a vertical format and select the correct answer. Reduce 7y 2y2 - 7 by 3 - 4y. 2 y2 - 11 y 10 -2 y2 11 y - 10 2 y2 11 y - 10 -2 y2 - 11 y 10.

Answer 1

You can use the fact that only the like terms of the polynomial get added or subtracted by adding or subtracting their coefficients.

The reduced form of the given polynomials' subtraction is given by

Option B: $11y - 10 + 2y^2$

What are like terms?

Those terms which have same variables raised with same powers.

For example,

$6x^2$ and $5x^2$ are like terms since variable is same, and it is raised to same power 2.

For example

$4x^3$ and $5x$ are not like terms as the variables are same but powers aren't same.

What are coefficients?

Constants who are in multiplication with variables are called coefficients of those variables.

For example, in

$10x^2$

we have 10 as coefficient of  $x^2$

When can we add or subtract terms of polynomial by their coefficient's addition or subtraction?

Suppose we have $5x^2 + 6y$ . Since those terms are not like terms, their coefficient won't be add and the expression we've got right now, is its simplest form and cannot be reduced more.

If we have, suppose, $4x + 5x^2 + 2x$, then we see that 4x and 2x are like terms, their coefficient can be added and thus, the simplified form would be $(4+2)x + 5x^2 = 6x + 5x^2$

Using the above facts to get the reduced form of the subtraction of both polynomials

The given polynomials to be subtracted are

$7y +2y^2 - 7\: \rm by\: 3 - 4y$

The subtraction will be done as:

$\begin{aligned}7y + 2y^2 - 7 - (3-4y) &= 7y + 2y^2 - 7 - 3 + 4y \\&= (7+4)y + 2y^2 -7-3 \\&= 11y + 2y^2 - 10\\\end{algned}$

Thus, the reduced form of the given polynomials' subtraction is given by

Option B: $11y - 10 + 2y^2$

Learn more about polynomial subtraction here:
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