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Identity IV is given by ( x + a) (x + b) = x 2 + (a + b)x + ab Replacing 'a' by (-c) and 'b' byr (-c), we have (x - c) (x - c) = x 2 + [(-c) + (-c)] x + [(-c) x (-c)] = x 2 + [-12c]x + (c 2 ) = x 2 - 2cx + c 2 Which is same as identity II.

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Algebraic Expressions and Identities

Short Answer Type

81.

Simplify:

(x + y) (x²-xy + y²)

121 Views

82.

Simplify:

(1.5x - 4y) (1.5x + 4y + 3) - 4.5x + 12y

376 Views

83.

Simplify:

(a +b + c)(a + b + c)

128 Views

84.

Find the product of

(i) ( 3a + 4b) and (2a + 3b)

(ii) ( x - 4) and ( 2x +3)

107 Views

85.

Multiply : ( x - y) and ( 3x + 5y)

96 Views

86.

Multiply :

(i) (a + 7) and ( b -5)

(ii) ( a²+ 2b²)9 and ( 5a - 3b)

132 Views

87.

Simplify :

(i) (a + 7) (a²+ 3a + 5)

(ii) (a + b) (2a - 3b + c) - (2a - 3b)c

226 Views

88.

Verify Identity (IV), for a = 2, b = 3, x = 5.

235 Views

89.

Consider the special case of Identity (IV) with a = b, what do you get? Is it related to Identity (1)?

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90.
Consider, the special case of Identity (IV) with a = –c and b = –c. What do you get? Is it related to Identity (II)?

Identity IV is given by
           ( x + a) (x + b) = x²+ (a + b)x + ab

Replacing 'a' by (-c) and 'b' byr (-c), we have

(x - c) (x - c) = x²+ [(-c) + (-c)] x + [(-c) x (-c)]
                   = x²+ [-12c]x + (c²)
                   = x²- 2cx + c²

Which is same as identity II.