Distributive Property on Algebraic Expression & Factorial Expressions
Distributive Property on Algebraic Expression & Factorial Expressions
Level:
Hard
No. of Questions5
Maximum Points10
Question 1 of 5
1. Question
A rectangular landing platform for a rocket is 50 yards wide and has an area of (50x + 2500) square yards. Write an expression that represents the perimeter (in yards) of the platform.
(Note: There can be more than one correct options)
Incorrect
Correct
1.
2.
3.
4.
GOOD GOING.
EXPLANATION
Factor the width of 50 yards out of the given area expression to find an expression that represents the length (in yards) of the platform.
50x + 2500
= 50 ⋅ x + 50 ⋅ 50
Rewrite the expression.
= 50(x + 50)
Distributive Property
So, the length (in yards) of the platform can be represented by x + 50.
Use the perimeter formula to write an expression that represents the
perimeter of the platform.
P
= 2ℓ+ 2w
Perimeter of a rectangle
= 2(x + 50) + 2(50)
Substitute for ℓ and w.
= 2x + 100 + 100
Multiply.
= 2x + 200
Add.
So, an expression that represents the perimeter (in yards) of the
platform is 2x + 200.
2x + 200 can be written as 200 + 2x as well.
Hence, 2x + 200 and 200 + 2x are the correct answers.
KEEP UP THE WORK, AND YOU’LL GET IT!
EXPLANATION
Factor the width of 50 yards out of the given area expression to find an expression that represents the length (in yards) of the platform.
50x + 2500
= 50 ⋅ x + 50 ⋅ 50
Rewrite the expression.
= 50(x + 50)
Distributive Property
So, the length (in yards) of the platform can be represented by x + 50.
Use the perimeter formula to write an expression that represents the
perimeter of the platform.
P
= 2ℓ+ 2w
Perimeter of a rectangle
= 2(x + 50) + 2(50)
Substitute for ℓ and w.
= 2x + 100 + 100
Multiply.
= 2x + 200
Add.
So, an expression that represents the perimeter (in yards) of the
platform is 2x + 200.
2x + 200 can be written as 200 + 2x as well.
Hence, 2x + 200 and 200 + 2x are the correct answers.
Question 2 of 5
2. Question
Which of the following expressions is equivalent to
(3x × (2y + 1) + 5x)?
Incorrect
Correct
1.
2.
3.
4.
GOOD GOING.
EXPLANATION
(3x × (2y + 1) + 5x)
= 3x × 2y + 3x ×1 + 5x
Apply distributive Property
= 6xy + 3x + 5x
Multiply
= 6xy + 8x
Add
Hence, (3x × (2y + 1) + 5x) = 6xy + 8x
GO FURTHER, YOU CAN BE A CHAMP!
EXPLANATION
(3x × (2y + 1) + 5x)
= 3x × 2y + 3x ×1 + 5x
Apply distributive Property
= 6xy + 3x + 5x
Multiply
= 6xy + 8x
Add
Hence, (3x × (2y + 1) + 5x) = 6xy + 8x
Hint
The distributive property is as follows: a(b+c) = ab + ac
Question 3 of 5
3. Question
Factorize the following expression
(3x × (2y + 1) + 5x)
(Note: There can be more than one correct options)
Incorrect
Correct
1.
2.
3.
4.
GOOD GOING.
EXPLANATION
(3x × (2y + 1) + 5x)
= 3x × 2y + 3x × 1 + 5x
Apply distributive Property
= 6xy + 3x + 5x
Multiply
= 6xy + 8x
Add
= 2x(3y + 4)
Simplify
2x(3y + 4) can be written 2x(4 + 3y) as well.
Hence, 2x(3y + 4) and 2x(4 + 3y) are the correct answers.
KEEP TRYING.
EXPLANATION
(3x × (2y + 1) + 5x)
= 3x × 2y + 3x × 1 + 5x
Apply distributive Property
= 6xy + 3x + 5x
Multiply
= 6xy + 8x
Add
= 2x(3y + 4)
Simplify
2x(3y + 4) can be written 2x(4 + 3y) as well.
Hence, 2x(3y + 4) and 2x(4 + 3y) are the correct answers.
Hint
The distributive property is as follows: a(b+c) = ab + ac
Question 4 of 5
4. Question
Factorize the expression (3x × (2y + 1) + 5x).
(Note: There can be more than one correct options)
Incorrect
Correct
1.
2.
3.
4.
YOU’RE DOING GREAT. KEEP GOING.
EXPLANATION
(3x × (2y + 1) + 5x)
= 3x × 2y + 3x ×1 + 5x
Apply distributive Property
= 6xy + 3x + 5x
Multiply
= 6xy + 8x
Add
= 2x(3y + 8)
Simplify
Hence, (3x × (2y + 1) + 5x) = 2x(3y + 8)
2x(3y + 8) can be written as (3y + 8) × 2x.
Hence, 2x × (3y + 8) and (3y + 8) × 2x are the correct answers.
GIVE IT ANOTHER TRY.
EXPLANATION
(3x × (2y + 1) + 5x)
= 3x × 2y + 3x ×1 + 5x
Apply distributive Property
= 6xy + 3x + 5x
Multiply
= 6xy + 8x
Add
= 2x(3y + 8)
Simplify
Hence, (3x × (2y + 1) + 5x) = 2x(3y + 8)
2x(3y + 8) can be written as (3y + 8) × 2x.
Hence, 2x × (3y + 8) and (3y + 8) × 2x are the correct answers.
Question 5 of 5
5. Question
Which of the following expressions is equivalent to
(3(2y + 1 + 6x) + 5x(2y - 3z - 2)?
