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(x + y) (x 2 -xy + y 2 ) = x(x 2 - xy + y 2 ) + y(x 2 - xy + y 2 ) = ( x X x 2 ) - (x X xy) + ( x X y 2 ) + (y x X 2 ) - ( y X xy) + (y x y 2 ) = x 3 - x 2 y + xy 2 + yx 2 - xy 2 + y 3 = x 3 + (- x 2 y + x 2 y )+ (xy 2 - xy 2 )+ y 3 = x 3 + 0 + 0 + y 3 = x 3 + y3

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Algebraic Expressions and Identities

Short Answer Type

81.
Simplify:

(x + y) (x²-xy + y²)

(x + y) (x²-xy + y²)

= x(x²- xy + y²) + y(x²- xy + y² )

= ( x X x²) - (x X xy) + ( x X y²) + (y x X²) - ( y X xy) + (y x y²)
= x³- x²y + xy² + yx² - xy²+ y³
= x³ + (- x²y + x²y )+ (xy² - xy² )+ y³= x³ + 0 + 0 + y³= x³ + y3

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82.

Simplify:

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

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83.

Simplify:

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

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84.

Find the product of

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

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

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85.

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

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86.

Multiply :

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

(ii) ( a²+ 2b²)9 and ( 5a - 3b)

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87.

Simplify :

(i) (a + 7) (a²+ 3a + 5)

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

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88.

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

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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)?

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Short Answer Type

81. Simplify:(x + y) (x2 -xy + y2 )

81.
Simplify:

(x + y) (x²-xy + y²)