Like terms : The terms having the same literal factors are called like or similar terms.
In the algebraic expression 12a2 – 15b2 + b2 –17a2 + 8ab + 9, we have, 12a2 and –17a2 as like terms and also – 15b2 and b2 are like terms. 

Unlike terms :  The terms not having same literal factors are called unlike or dissimilar terms.

In the algebraic expression 3p2q + 5pq2 – 7pq – 9qp2, 5pq2 and –7pq are unlike terms.

Types of algebraic expressions. Trinomials

A trinomial algebraic expression is an algebraic expression that has three terms.
The prefix 'tri' in 'trinomial' stands for 3 terms.
To add two trinomials, you must:
 1) remove the brackets (without changing the signs, because the “+” sign is in front of the brackets);
2) add the like terms.

Example:
Add trinomials: 

(−5x3+3y−5y2)+(8x3+5y2−2y)

1) Remove the brackets:
(−5x3+3y−5y2)+(8x3+5y2−2y)==−5x3+3y−5y2+8x3+5y2−2y.

2) Find the like terms and add:
−5x3¯¯¯¯¯¯¯¯+3y−5y2+8x3¯¯¯¯¯¯¯¯+5y2−2y=3x3+3y¯¯¯¯¯¯−5y2+5y2−2y¯¯¯¯¯¯=3x3+y.
To multiply a trinomial by a trinomial, you need to multiply each term of one trinomial by each terms of another trinomial and add the resulting products. 
(a+b+c)⋅ (d+e+f)==ad + ae +af +bd +be +bf +cd +ce +cf = ad + ae + af + bd + be + bf + cd + ce + cf

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 (7x2+3x−2) and −2x2+2x+3

1) Write down the difference of the trinomials and remove the brackets, taking the signs before the brackets into account:
(7x2+3x−2)−(−2x2+2x+3)=7x2+3x−2+2x2−2x−3

2) Find the like terms:
7x2¯¯¯¯¯+3x¯¯¯¯¯¯¯¯−2 +2x2¯¯¯¯¯−2x¯¯¯¯¯¯¯¯−3

3) Combine the like terms:
7x2¯¯¯¯¯+3x¯¯¯¯¯¯¯¯¯¯¯¯−2+2x2¯¯¯¯¯¯¯¯−2x¯¯¯¯¯¯¯¯¯¯¯¯−3=(7+2)x2+(3−2)x−2−3=9x2+1x−5

4) If the coefficient of a term is 1, then usually we do not write it:
9x2+1x−5=9x2+x−5

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clas 7 math
Medha Sharma

Course : CBSE Class 7

Start Date : 09.02.2023

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