Algebraic Identities
Math ⇒ Algebra
Algebraic Identities starts at 7 and continues till grade 12.
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Prove that (a + b + c)2 = a2 + b2 + c2 + 2ab + 2bc + 2ca.
Prove that (a + b)3 + (a - b)3 = 2a3 + 6ab2.
State the algebraic identity for the difference of squares.
Which identity is used to expand (a + b)3?
If (a + b)2 = 36 and (a - b)2 = 16, what is the value of ab?
If (a + b)2 = 49 and (a - b)2 = 9, find the value of ab.
If a = 1 and b = -2, calculate (a - b)2 using the identity.
If a = 2 and b = -3, calculate the value of (a + b)2 using the identity.
Which of the following is NOT an algebraic identity?
(1) (a + b)2 = a2 + 2ab + b2
(2) (a - b)2 = a2 - 2ab + b2
(3) (a + b)3 = a3 + b3
(4) a2 - b2 = (a - b)(a + b)
Which of the following is the correct expansion of (a - b)2?
(1) a2 - 2ab + b2
(2) a2 + 2ab + b2
(3) a2 - ab + b2
(4) a2 + ab + b2
Which of the following is the correct expansion of (a + b + c)2?
(1) a2 + b2 + c2 + 2ab + 2bc + 2ca
(2) a2 + b2 + c2 + ab + bc + ca
(3) a2 + b2 + c2 + 2ab + 2bc
(4) a2 + b2 + c2
Which of the following is the correct expansion of (a+b)3?
(1) a3 + 3a2b + 3ab2 + b3
(2) a3 + b3
(3) a3 + 2ab + b3
(4) a3 + 3ab2 + b3
Fill in the blank: (a - b)3 = a3 - 3a2b + 3ab2 - _________.
Fill in the blank: (a + b + c)2 = a2 + b2 + c2 + 2ab + 2bc + _________.
Fill in the blank: (a + b)(a - b) = _________.
Fill in the blank: (a + b)2 = a2 + ________ + b2.
The expansion of (a - b)3 is a3 - 3a2b + 3ab2 - b3. Yes or No?
The identity (a + b)2 = a2 + 2ab + b2 can be used to expand (3x + 4y)2. True or False?
The identity (a + b)2 = a2 + 2ab + b2 is valid for all real numbers a and b. True or False?
The identity (a + b)3 = a3 + 3a2b + 3ab2 + b3 can be used to expand (x + y)3. True or False?
