Subtraction of trinomials — lesson. Mathematics CBSE, Class 7.

UPSKILL MATH PLUS

Learn Mathematics through our AI based learning portal with the support of our Academic Experts!

To subtract two trinomials, you must:

1) remove the brackets and change the signs of the trinomials that are preceded by the sign "\(- \)" to the opposite;
2) combine the like terms of the trinomials.

Example:

Let us calculate the difference of trinomials

(7 x^{2} + 3 x - 2)

and

- 2 x^{2} + 2 x + 3

1) Write down the difference of the trinomials and remove the brackets, taking the signs before the brackets into account:

(7 x^{2} + 3 x - 2) - (- 2 x^{2} + 2 x + 3) = 7 x^{2} + 3 x - 2 + 2 x^{2} - 2 x - 3

2) Find the like terms:

\underline{7 x^{2}} + \underline{\underline{3 x}} - \underset{⏟}{2} + \underline{2 x^{2}} - \underline{\underline{2 x}} - \underset{⏟}{3}

3) Combine the like terms:

\underline{7 x^{2}} \underline{\underline{+ 3 x}} - 2 \underline{+ 2 x^{2}} \underline{\underline{- 2 x}} - 3 = (7 + 2) x^{2} + (3 - 2) x - 2 - 3 = 9 x^{2} + 1 x - 5

4) If the coefficient of a term is \(1\), then usually we do not write it:

9 x^{2} + 1 x - 5 = 9 x^{2} + x - 5

Important!

Remember: the sum or the difference of trinomials is always a trinomial.

To find the opposite of a trinomial, change the signs of the coefficients of all terms to the opposite.

Example:

The opposite of

- 2 m^{2} n + 3 mn - 4

2 m^{2} n - 3 mn + 4

The opposite of

7 a^{2} - 2,5 a - 8

- 7 a^{2} + 2,5 a + 8

The opposite of

x^{n} - 0,05

- x^{n} + 0,05

Two trinomials are called opposite if their sum is \(0\).

Example:

Trinomials

- 4 a^{2} b + 3 ab + 2

and

4 a^{2} b - 3 ab - 2

are opposite, because their sum is zero:

(- 4 a^{2} b + 3 ab + 2) + (4 a^{2} b - 3 ab + - 2) =

\begin{array}{l} - 4 a^{2} b + 3 ab + 2 + 4 a^{2} b - 3 ab - 2 = \\ = 3 ab + 2 - 3 ab - 2 = 2 - 2 = 0 \end{array}

Previous theory

Exit to the topic

Next exercise

Send feedback

Did you find an error?

Send it to us!

3. Subtraction of trinomials

Theory: