SOLUTION: Monomials adding subtracting muliplying and dividing ... - Free Printable

Let's solve each part step by step.

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B. Find the sum of the following:

We combine like terms (terms with the same variables and exponents).

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1. $ 4a + 2a + (-5a) $
= $ (4 + 2 - 5)a = 1a = \boxed{a} $

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2. $ 7x + (-3x) + 5x $
= $ (7 - 3 + 5)x = 9x = \boxed{9x} $

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3. $ -3y + 4y + 2y $
= $ (-3 + 4 + 2)y = 3y = \boxed{3y} $

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4. $ 4b + (-5b) + (-2b) $
= $ (4 - 5 - 2)b = (-3)b = \boxed{-3b} $

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5. $ -4xy + 5xy + 3xy $
= $ (-4 + 5 + 3)xy = 4xy = \boxed{4xy} $

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6. $ 4ab - 9ab + 12ab $
= $ (4 - 9 + 12)ab = 7ab = \boxed{7ab} $

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7. $ -9x^2 + 10x^2 + 18x^2 $
= $ (-9 + 10 + 18)x^2 = 19x^2 = \boxed{19x^2} $

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8. $ -3rs + 15rs + 20rs $
= $ (-3 + 15 + 20)rs = 32rs = \boxed{32rs} $

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9. $ 130d + (-130d) + 50d $
= $ (130 - 130 + 50)d = 50d = \boxed{50d} $

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10. $ -40ab + 39ab + 2ab $
= $ (-40 + 39 + 2)ab = 1ab = \boxed{ab} $

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✔ B Answers:

1. $ a $
2. $ 9x $
3. $ 3y $
4. $ -3b $
5. $ 4xy $
6. $ 7ab $
7. $ 19x^2 $
8. $ 32rs $
9. $ 50d $
10. $ ab $

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C. Fill in the blanks:

We need to find the missing expression that makes each equation true.

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1. $ 40x + \_\_\_\_ = -15x $
Let the blank be $ x $. Then:
$ 40x + x = -15x $ → $ x = -15x - 40x = -55x $
So, $ \boxed{-55x} $

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2. $ -10x + 38x = \_\_\_\_ $
= $ 28x = \boxed{28x} $

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3. $ -25y + (-10y) = \_\_\_\_ $
= $ -35y = \boxed{-35y} $

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4. $ 14a + \_\_\_\_ = -2a $
Let blank be $ x $. Then:
$ 14a + x = -2a $ → $ x = -2a - 14a = -16a $
So, $ \boxed{-16a} $

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5. $ -16b + \_\_\_\_ = 20b $
Let blank be $ x $. Then:
$ -16b + x = 20b $ → $ x = 20b + 16b = 36b $
So, $ \boxed{36b} $

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6. $ \_\_\_\_ + 15c = -15c $
Let blank be $ x $. Then:
$ x + 15c = -15c $ → $ x = -15c - 15c = -30c $
So, $ \boxed{-30c} $

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7. $ 20x^2 + \_\_\_\_ = -8x^2 $
Let blank be $ x $. Then:
$ 20x^2 + x = -8x^2 $ → $ x = -8x^2 - 20x^2 = -28x^2 $
So, $ \boxed{-28x^2} $

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8. $ -18xy + \_\_\_\_ = 12xy $
Let blank be $ x $. Then:
$ -18xy + x = 12xy $ → $ x = 12xy + 18xy = 30xy $
So, $ \boxed{30xy} $

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9. $ 40x^2y + (-15x^2y) = \_\_\_\_ $
= $ (40 - 15)x^2y = 25x^2y = \boxed{25x^2y} $

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10. $ \_\_\_\_ + (-8xy) = -20xy $
Let blank be $ x $. Then:
$ x - 8xy = -20xy $ → $ x = -20xy + 8xy = -12xy $
So, $ \boxed{-12xy} $

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✔ C Answers:

1. $ -55x $
2. $ 28x $
3. $ -35y $
4. $ -16a $
5. $ 36b $
6. $ -30c $
7. $ -28x^2 $
8. $ 30xy $
9. $ 25x^2y $
10. $ -12xy $

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✔ Final Answer Summary:

#### B. Sum of expressions:
1. $ a $
2. $ 9x $
3. $ 3y $
4. $ -3b $
5. $ 4xy $
6. $ 7ab $
7. $ 19x^2 $
8. $ 32rs $
9. $ 50d $
10. $ ab $

#### C. Fill in the blanks:
1. $ -55x $
2. $ 28x $
3. $ -35y $
4. $ -16a $
5. $ 36b $
6. $ -30c $
7. $ -28x^2 $
8. $ 30xy $
9. $ 25x^2y $
10. $ -12xy $

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