Directions: Simplify each of the following expression.
1. c²-b
2. c+a³
3.a⁴-b
pls help me answer
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Directions: Simplify each of the following expression.
1. c²-b
2. c+a³
3.a⁴-b
pls help me answer
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1. c²-b
Step by Step Solution
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STEP
1
:
Trying to factor as a Difference of Squares:
1.1 Factoring: c2-b
Theory : A difference of two perfect squares, A2 - B2 can be factored into (A+B) • (A-B)
Proof : (A+B) • (A-B) =
A2 - AB + BA - B2 =
A2 - AB + AB - B2 =
A2 - B2
Note : AB = BA is the commutative property of multiplication.
Note : - AB + AB equals zero and is therefore eliminated from the expression.
Check : c2 is the square of c1
Check : b1 is not a square !!
Ruling : Binomial can not be factored as the difference of two perfect squares
Final result :
c2 - b
2. c+a³
Step by Step Solution
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STEP
1
:
Trying to factor as a Sum of Cubes:
1.1 Factoring: c+a3
Theory : A sum of two perfect cubes, a3 + b3 can be factored into :
(a+b) • (a2-ab+b2)
Proof : (a+b) • (a2-ab+b2) =
a3-a2b+ab2+ba2-b2a+b3 =
a3+(a2b-ba2)+(ab2-b2a)+b3=
a3+0+0+b3=
a3+b3
Check : c 1 is not a cube !!
Ruling : Binomial can not be factored as the difference of two perfect cubes
Final result :
c + a3
3.a⁴-b
Step by Step Solution
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STEP
1
:
Trying to factor as a Difference of Squares:
1.1 Factoring: a4-b
Theory : A difference of two perfect squares, A2 - B2 can be factored into (A+B) • (A-B)
Proof : (A+B) • (A-B) =
A2 - AB + BA - B2 =
A2 - AB + AB - B2 =
A2 - B2
Note : AB = BA is the commutative property of multiplication.
Note : - AB + AB equals zero and is therefore eliminated from the expression.
Check : a4 is the square of a2
Check : b1 is not a square !!
Ruling : Binomial can not be factored as the difference of two perfect squares
Final result :
a4 - b