Certainly! Let's consider two trinomial expressions of the form [tex]\( ax + by + c \)[/tex].
We define the first trinomial expression as:
[tex]\[ \text{Expression 1: } 2x + 5y + 7 \][/tex]
And the second trinomial expression as:
[tex]\[ \text{Expression 2: } 3x + y + 4 \][/tex]
Now, let's find the sum of these two trinomial expressions. We add the corresponding coefficients of [tex]\( x \)[/tex], [tex]\( y \)[/tex], and the constant terms.
1. Add the coefficients of [tex]\( x \)[/tex]:
[tex]\[ 2 + 3 = 5 \][/tex]
2. Add the coefficients of [tex]\( y \)[/tex]:
[tex]\[ 5 + 1 = 6 \][/tex]
3. Add the constant terms:
[tex]\[ 7 + 4 = 11 \][/tex]
So, the sum of the two trinomial expressions is:
[tex]\[ (2x + 5y + 7) + (3x + y + 4) = 5x + 6y + 11 \][/tex]
Next, let's find the difference of these two trinomial expressions. We subtract the corresponding coefficients of [tex]\( x \)[/tex], [tex]\( y \)[/tex], and the constant terms of the second expression from the first.
1. Subtract the coefficients of [tex]\( x \)[/tex]:
[tex]\[ 2 - 3 = -1 \][/tex]
2. Subtract the coefficients of [tex]\( y \)[/tex]:
[tex]\[ 5 - 1 = 4 \][/tex]
3. Subtract the constant terms:
[tex]\[ 7 - 4 = 3 \][/tex]
So, the difference of the two trinomial expressions is:
[tex]\[ (2x + 5y + 7) - (3x + y + 4) = -x + 4y + 3 \][/tex]
In summary:
- The sum of the trinomials [tex]\( 2x + 5y + 7 \)[/tex] and [tex]\( 3x + y + 4 \)[/tex] is [tex]\( 5x + 6y + 11 \)[/tex].
- The difference of the trinomials [tex]\( 2x + 5y + 7 \)[/tex] and [tex]\( 3x + y + 4 \)[/tex] is [tex]\( -x + 4y + 3 \)[/tex].
