To find the missing coefficient in the given expression:
[tex]\[
(15x^2 + 11y^2 + 8x) - (7x^2 + 5y^2 + 2x)
\][/tex]
we need to follow these steps:
1. Subtract the coefficients of [tex]\( x^2 \)[/tex]:
- Coefficient of [tex]\( x^2 \)[/tex] in the first expression: [tex]\( 15 \)[/tex]
- Coefficient of [tex]\( x^2 \)[/tex] in the second expression: [tex]\( 7 \)[/tex]
[tex]\[
15 - 7 = 8
\][/tex]
2. Subtract the coefficients of [tex]\( y^2 \)[/tex]:
- Coefficient of [tex]\( y^2 \)[/tex] in the first expression: [tex]\( 11 \)[/tex]
- Coefficient of [tex]\( y^2 \)[/tex] in the second expression: [tex]\( 5 \)[/tex]
[tex]\[
11 - 5 = 6
\][/tex]
3. Subtract the coefficients of [tex]\( x \)[/tex]:
- Coefficient of [tex]\( x \)[/tex] in the first expression: [tex]\( 8 \)[/tex]
- Coefficient of [tex]\( x \)[/tex] in the second expression: [tex]\( 2 \)[/tex]
[tex]\[
8 - 2 = 6
\][/tex]
Putting everything together, the resulting expression after subtraction is:
[tex]\[
(15x^2 + 11y^2 + 8x) - (7x^2 + 5y^2 + 2x) = 8x^2 + 6y^2 + 6x
\][/tex]
Therefore, the missing coefficient in the expression is [tex]\( 8 \)[/tex].
