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Algebraic Expressions and Identities

Short Answer Type

61.

Find the product of:

(i) 2x, 5y and 7z (ii) 4xy, 5x²y² and 6x³y³

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62.

Multiply:

(i) (–3x) and (–5y + 2) (ii) 5xy and (y² + 3)

126 Views

63.

Simplify the expressions and evaluate them as directed:

(i) x(x – 3) + 2 for x = 1 (ii) 3y(2y – 7) – 3(y – 4) – 63 for y = –2.

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64.

Multiply (x – 2) and (2x + 3).

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65.
Simplify (a + b) (a - 2b + 3c) - (2a - 3b)c

∵   (a + b) ( a - 2b + 3c) = a x ( a - 2b + 3c) + b(a - 2b + 3c)
                                = a²- 2ab + 3ac + ab - 2b²+ 3bc
                                = a²+ (- 2ab + ab) + 3ac - 2b²+ 3bc
= a²- 2b² - ab + 3bc + 3ac

and    ( 2a - 3b) x c - 2ac - 3bc

∴ ( a +b) (a - 2b + 3c) - (2a - 3b) x c
         = (a²-2b²- ab + 3bc + 3ac) - (2ac + 3bc)
         = a²-2b²- ab + (3bc + 3ac) - (2ac + 3bc)
         = a²-2b²- ab + 3(bc + 3ac) + (3ac + 2ac)   ( Combining the like terms bc and ac)
        = a²-2b²- ab + (6bc) + (ac)
            = a²-2b²- ab + 6bc + ac