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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.

Here, Length = 3x²- 2
Breadth = 2x + 5

∴ Area = (Length) x ( Breadth)
                 = (3x²- 2) x (2x + 5)
                 = 3x²(2x + 5) + (-2)(2x +5)
                 = (3x²x 2x) + (5 x 3x²) + [(-2) x 2x + (-2) x 5]
                 = 6x³+ 15x²+ (-4x) +(-10)
                 = 6x³+ 15x²- 4x -10