Add:
5x2 + 3x – 8, 4x + 7 – 2x2
and 6 – 5x + 4x2
Answers
Answer:
1. Simplify: (4x2 - 2x) - (-5x2 - 8x).
Solution:
(4x2 - 2x) - (-5x2 - 8x)
= 4x2 - 2x + 5x2 + 8x.
= 4x2 + 5x2 - 2x + 8x.
= 9x2 + 6x.
= 3x(3x + 2).
Answer: 3x(3x + 2)
2. Simplify: (-7x2 - 3x) - (4x2 - x)
Solution:
(-7x2 - 3x) - (4x2 - x)
= -7x2 - 3x - 4x2 + x
= -7x2 - 4x2 - 3x + x
= -11x2 – 2x
= -x(11x + 2)
Answer: -x(11x + 2)
3. Simplify: (-5x2 - 8x + 7) - (5x2 - 4)
Solution:
(-5x2 - 8x + 7) - (5x2 - 4)
= -5x2 - 8x + 7 - 5x2 + 4
= -5x2 - 5x2 - 8x + 7 + 4
= -10x2 – 8x + 11
Answer: -10x2 – 8x + 11
4. Simplify: (4x2 + 5x) + (x2 - 5x + 1)
Solution:
(4x2 + 5x) + (x2 - 5x + 1)
= 4x2 + 5x + x2 - 5x + 1
= 4x2 + x2+ 5x - 5x + 1
= 5x2 + 0 + 1
= 5x2 + 1
Answer: 5x2 + 1
5. Simplify: (-6x + 3) - (-x2 + 5x)
Solution:
(-6x + 3) - (-x2 + 5x)
= -6x + 3 + x2 - 5x
= -6x - 5x + x2 + 3
= x2 – 11x + 3
Answer: x2 – 11x + 3
6. Simplify: (-9x - 5) - (-9x2 + x - 5)
Solution:
(-9x - 5) - (-9x2 + x - 5)
= -9x - 5 + 9x2 - x + 5
= 9x2 - 9x – x – 5 + 5
= 9x2 – 10x
= x(9x – 10)
Answer: x(9x – 10)
7. Simplify: (2x - 4) - (6x + 6)
Solution:
(2x - 4) - (6x + 6)
= 2x - 4 - 6x – 6
= 2x – 6x – 4 – 6
= -4x – 10
= -2(2x + 5)
Answer: -2(2x + 5)
8. Simplify:(8+4x)/4x
Solution:
(8+4x)/4x
= 4(2 + x)/4x
[Cancel 4 from the numerator and denominator]
= (2 + x)/x
Answer: (2 + x)/x
9. Decide whether the lines are parallel, perpendicular or neither.
x + 4y = 7 and 4x – y = 3
Solution:
x + 4y = 7
4y = -x + 7
y = (-1/4) x + 7
Slope of the equation x + 4y = 7 is -1/4.
Again, 4x – y = 3
y = 4x – 3
Slope of the equation 4x – y = 3 is 4.
Since multiplying both the slope of the equation = -1/4 × 4 = -1
Therefore, the given two equations are perpendicular to each other.
Answer: Perpendicular
10. Simplify: 3x – 5 + 23x – 9
Solution:
Explanation:
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