The document Extra Questions- Comparing Quantities Class 8 Notes | EduRev is a part of the Class 8 Course Mathematics (Maths) Class 8.

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**Question 1:** Add: a + b + ab ; b – c + bc and c + a + ac

**Solution:** We have :

Thus, the sum of the given expressions is 2a + 2b + ab + bc + ca.

**Question 2:** Verify the identity (x + a)( x + b) = x^{2} + (a + b)x + ab for a = 2, b = 3 and x = 4,

**Solution: **We have

(x + a)(x + b) = x^{2} + (a + b)x + ab

Puting x = 2, b = 3 and x = 4, we have

LHS = (x + a)(x + b)

= (4 + 2)(4 + 3)

= 6 * 7 = 42

RHS = x^{2} + (a + b)x + ab

= (4)^{2} + (2 + 3)4 + (2 * 3)

= 16 + 5 * 4 + 6

= 16 + 20 + 6 = 42

i.e. LHS = RHS

Thus, the given identity is true for the given values.

**Question 3:** Using a suitable identity to get the product:

**Solution:** Using the identity (a – b)^{2} = a^{2} – 2ab + b^{2}, we have

**Question 4: **The length and breadth of a rectangle are 3x^{2} – 2 and 2x + 5 respectively. Find its area.

**Solution:** Here,

Length = 3x^{2} – 2

Breadth = 2x + 5

∴ Area = (Length) * (Breadth)

= (3x^{2} – 2) * (2x + 5)

= 3x^{2}(2x + 5) + (–2)(2x + 5)

= (3x^{2} * 2x) + (5 * 3x^{2}) + [(–2) * 2x + (–2) * 5]

= 6x^{3} + 15x^{2} + (–4x) + (–10) = 6x^{3} + 15x^{2} – 4x – 10

Thus, the required area of the rectangle is 6x^{3} + 15x^{2} – 4x – 10 sq. units.

**Question 5:** Find the volume of cuboid whose dimensions are (x^{2} – 2); (2x + 2) and (x – 1).

**Solution:** ∵ Volume of a cuboid = Length * Breadth * Height

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