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Algebraic Expressions and Identities

Short Answer Type

151.

Subtract 4p²q + 5pq² – 3pq + 7q – 8p – 10 from 5p²q – 2pq² + 5pq – 11q – 3p + 28

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152.

Find the product of (5p² + 4p + 7) and (p + 2).

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153.

Simplify 3x(2x – 1) + 8 and find its values at x = –1.

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154.

Simplify: (x² – 6)(x – 6) + 36

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155.

Verify the identity (x + a)( x + b) = x² + (a + b)x + ab for a = 2, b = 3 and x = 4,

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156.

The length and breadth of a rectangle are 3x² – 2 and 2x + 5 respectively. Find its area.

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157.
Find the volume of cuboid whose dimensions are (x² – 2); (2x + 2) and (x – 1).

∵ Volumen of a cubiod = Length x Breadtj x Height
= (x²- 1) x (2x + 2) x (x - 1)

                                 = [(x²- 1) x (2x + 2)] x (x - 1)
                                 = [2x³- 2x- 2x² - 2) X (x - 1)
                                 = x(2x³+ 2x²- 2x - 2) X (x - 1)
                                 = 2x⁴+ 2x³- 2x² - 2x) - 1(2x³+ 2x²- 2x - 2)
                                 = 2x⁴+ 2x³- 2x² - 2x - 2x³- 2x²+ 2x + 2)
                                 = 2x⁴- 2x²- 2x² + 2
                                 = 2x⁴- 4x² + 2