Answer:
12a. Addition = 7y⁵ + 7y³ – 6y – 5
12b. Subtraction = – y⁵ – 3y³ + 8y + 11
13a. Addition = 5x⁴ + x³ – 6x² + 8x + 17
13b. Subtraction = – x⁴ – 9x³ –6x² + 8x + 3
14a. Addition = – 2b⁴ + b³ – 11b² – 1
14b. Subtraction = 4b⁴ + 7b³ – b² + 8b – 1
15a. Addition = m⁵ + m⁴ + m³ + m²
15b. Subtraction = m⁵ – m⁴ – m³ – m² – 10
16a. Addition = 4x⁴ + 12x³ + 18x² + 16x + 4
16b. Subtraction = 4x⁴ – 4x³ + 14x² – 16x + 4
Step-by-step explanation:
12a. Addition
.. 3y⁵ + 2y³ + y + 3
+ (4y⁵ + 5y³– 7y – 8)
————————————
= 7y⁵ + 7y³ – 6y – 5
12b. Subtraction
.. 3y⁵ + 2y³ + y + 3
– (4y⁵ + 5y³– 7y – 8)
¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯
= – y⁵ – 3y³ + 8y + 11
13a. Addition
.. 2x⁴ – 4x³ – 6x² + 8x + 10
+ (3x⁴ + 5x³ +...................+ 7)
¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯
= 5x⁴ + x³ – 6x² + 8x + 17
13b. Subtraction
.. 2x⁴ – 4x³ – 6x² + 8x + 10
– (3x⁴ + 5x³ +...................+ 7)
¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯
= – x⁴ – 9x³ – 6x² + 8x + 3
14a. Addition
...... b⁴ + 4b³ – 6b² + 4b – 1
+ (– 3b⁴ – 3b³ – 5b² – 4b)
¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯
= – 2b⁴ + b³ – 11b² – 1
14b. Subtraction
...... b⁴ + 4b³ – 6b² + 4b – 1
– (– 3b⁴ – 3b³ – 5b² – 4b)
¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯
= 4b⁴ + 7b³ – b² + 8b – 1
15a. Addition
... m⁵ + m³ – 5
+ (m⁴ + m² + 5)
¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯
= m⁵ + m⁴ + m³ + m²
15b. Subtraction
... m⁵ + m³ – 5
– (m⁴ + m² + 5)
¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯
= m⁵ – m⁴ – m³ – m² – 10
16a. Addition
.... 4x⁴ + 8x³ + 16x² + 4
+ (4x³ + 2x² + 16x)
¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯
= 4x⁴ + 12x³ + 18x² + 16x + 4
16b. Subtraction
.... 4x⁴ + 8x³ + 16x² + 4
– (4x³ + 2x² + 16x)
¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯
= 4x⁴ – 4x³ + 14x² – 16x + 4
is basically the number that is to be found.