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Pls tell me 4 identities for integers.
Answers
Answer:
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Step-by-step explanation:
The four identities are as follows.
(a + b)2 = a2 + 2ab + b2
(a + b)2 = a2 + 2ab + b2
(a + b)(a - b) = a2ic - b2
(x + a)(x + b) = x2 + x(a + b) + ab.
Answer:
The major Properties/ Identities of Integers are:
Closure Property
Associative Property
Commutative Property
Distributive Property
Additive Inverse Property
Multiplicative Inverse Property
Step-by-step explanation:
*Closure Property
According to the closure property of integers, when two integers are added or multiplied together, it results in an integer only. If a and b are integers, then:
a + b = integer
a x b = integer
Examples:
2 + 5 = 7 (is an integer)
2 x 5 = 10 (is an integer)
*Commutative Property
According to the commutative property of integers, if a and b are two integers, then:
a + b = b + a
a x b = b x a
Examples:
3 + 8 = 8 + 3 = 11
3 x 8 = 8 x 3 = 24
But for the commutative property is not applicable to subtraction and division of integers.
*Associative Property
As per the associative property , if a, b and c are integers, then:
a+(b+c) = (a+b)+c
ax(bxc) = (axb)xc
Examples:
2+(3+4) = (2+3)+4 = 9
2x(3×4) = (2×3)x4 = 24
Similar to commutativity, associativity is applicable for the addition and multiplication of integers only.
*Distributive property
According to the distributive property of integers, if a, b and c are integers, then:
a x (b + c) = a x b + a x c
Example: Prove that: 3 x (5 + 1) = 3 x 5 + 3 x 1
LHS = 3 x (5 + 1) = 3 x 6 = 18
RHS = 3 x 5 + 3 x 1 = 15 + 3 = 18
Since, LHS = RHS
Hence, proved.
*Additive Inverse Property
If a is an integer, then as per the additive inverse property of integers,
a + (-a) = 0
Hence, -a is the additive inverse of integer a.
*Multiplicative inverse Property
If a is an integer, then as per the multiplicative inverse property of integers,
a x (1/a) = 1
Hence, 1/a is the multiplicative inverse of integer a.
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