Question

part 2 mark up the like terms that could be combined in each row. you can do this by coloring like terms the same color or drawing the same annotation (circle, triangle,underline etc) then, write your simplified answer in the blanks. be careful of signs.
1 ( 4 a ^ { 2 } ) ( + 3 a ) ( - 16 a ) ( + 3 a ^ { 2 } )
2 ( 6 b ) ( - 2 b ) ( + 8 ) ( + 4 b )
3 ( 11 ) ( - 15 ) ( + 8 g ) ( + g )
4 ( 5 g ^ { 2 } ) ( + 6 g ) ( - g ) ( + 8 g ^ { 5 } )
5 ( 17 x ) ( - 6 y ) ( + 9 y ^ { 3 } ) ( - 8 x )
6 ( y ) ( + 8 ) ( - 6 y ) ( - 8 )
7 ( 2 x y ) ( + 9 x ) ( - 6 x y ) ( - 8 y )
8 ( 4 w ) ( - 8 w ) ( + x ) ( - 12 w )

Explanation:

Step1: Combine like terms for row 3

For the constants \(11\) and \(-15\), \(11-15=-4\). For the terms with \(g\), \(8g + g=(8 + 1)g=9g\).

Step2: Combine like terms for row 4

For the terms with \(g\), \(6g-g=(6 - 1)g = 5g\). The terms \(5g^{2}\) and \(8g^{5}\) have different exponents and cannot be combined with the \(g\) terms.

Step3: Combine like terms for row 5

For the terms with \(x\), \(17x-8x=(17 - 8)x=9x\). The terms \(-6y\) and \(9y^{3}\) cannot be combined with the \(x\) terms.

Step4: Combine like terms for row 6

For the terms with \(y\), \(y-6y=(1 - 6)y=-5y\). For the constants \(8-8 = 0\).

Step5: Combine like terms for row 7

For the terms with \(xy\), \(2xy-6xy=(2 - 6)xy=-4xy\). The terms \(9x\) and \(-8y\) cannot be combined with the \(xy\) terms.

Step6: Combine like terms for row 8

For the terms with \(w\), \(4w-8w-12w=(4-8 - 12)w=-16w\). The term \(x\) cannot be combined with the \(w\) terms.

Answer:

1. \(-4 + 9g\)
2. \(5g^{2}+5g + 8g^{5}\)
3. \(9x-6y + 9y^{3}\)
4. \(-5y\)
5. \(-4xy+9x - 8y\)
6. \(-16w+x\)