Archives

Simplify 3x (4x – 5) + 3 and find its values for (i) x = 3 (ii) x = 1/2

Answer: 3x (4x - 5) + 3 = (3x × 4x) - (3x × 5) + 3 3x (4x - 5) + 3 = 12x2 - 15x + 3 Substitute the value of (i) x = 3 in 12x2 -... View Article

Simplify a (a³ + a + 1) + 5 and find its value for (i) a = 0, (ii) a = 1 (iii) a = -1.

Answer: ⇒ (a × a2)+ (a × a) + (a + 1) + 5 ⇒ a3 + a2 + a + 5 Puting a = 0 in a3 + a2 + a + 5 a3 + a2 + a + 5 ⇒ 03 +... View Article

Simplify: (1.5x – 4y)(1.5x + 4y + 3) – 4.5x + 12y

Answer: 2.25x2 - 16y2 Consider (1.5x - 4y)(1.5x + 4y + 3) - 4.5x + 12y 2.25x2 + 6xy + 4.5x - 6xy - 16y2 - 12y - 4.5x + 12y = 2.25x2 - 16y2... View Article

Simplify: (2.5p – 1.5q)² – (1.5p – 2.5q)²

Answer: 4p2 - 4q2 Using the identities (a + b) 2 = a2 + b2 + 2ab (a - b) 2 = a2 + b2 - 2ab Consider (4m + 5n)2 Using identity (a - b) 2 = a2 +... View Article

Simplify: (2x + 5)² – (2x – 5)²

Answer: 40x Using the identities (a + b) 2 = a2 + b2 + 2ab (a - b) 2 = a2 + b2 - 2ab Consider (2x + 5)2 Using identity (a + b) 2 = a2 + b2 +... View Article

Simplify: (4m + 5n)² + (5m + 4n)²

Answer: 41m2 + 41n2 + 80mn Using the identities (a + b) 2 = a2 + b2 + 2ab (a - b) 2 = a2 + b2 - 2ab Consider (4m + 5n)2 Using identity... View Article

Simplify: (7m – 8n)² + (7m + 8n)²

Answer: 98m2 + 128n2 Using the identities (a + b) 2 = a2 + b2 + 2ab (a - b) 2 = a2 + b2 - 2ab Consider (7m - 8n)2 Using identity (a - b) 2 = a2... View Article

Simplify: (a + b + c)(a + b – c)

Answer: a2 + b2 - c2 + 2ab (a + b + c) × (a + b - c) = a × (a + b - c) + b × (a + b - c) + c × (a + b - c) = (a ×... View Article

Simplify: (a + b) (c – d) + (a – b) (c + d) + 2 (ac + bd)

Answer: 4ac (a + b) × (c – d) + (a - b) × (c + d) + 2 (ac + bd) = (a + b) × (c - d) + (a - b) × (c + d) + (2ac +... View Article

Simplify: (a² – b2)²

Answer: a4 + b4 - 2a2b2 Using the identity (a - b) 2 = a2 + b2 - 2ab (a2 - b2)2= (a2)2 + (b2)2 - 2 × a2 × b2 (a2 - b2)2 = a4 + b4 - 2a2b2... View Article

Simplify: (a² + 5) (b³ + 3) + 5

Answer: a2b3 + 5b3 + 3a2 + 20 (a2 + 5)(b3+ 3) (a2 + 5)(b3+ 3) = a2 × (b3+ 3) + 5 × (b3+ 3) (a2 + 5)(b3+ 3) = (a2 × b3) + (a2... View Article

Simplify: (ab + bc)²– 2ab²c

Answer: a2b2 + b2c2 Using the identities (a + b) 2 = a2 + b2 + 2ab (a - b) 2 = a2 + b2 - 2ab Consider (ab + bc)2 Using identity (a + b) 2 = a2... View Article

Simplify: (m² – n²m)² + 2m³n²

Answer: m4 + n4m2 Using the identities (a + b) 2 = a2 + b2 + 2ab (a - b) 2 = a2 + b2 - 2ab Consider (m2 - n2m)2 Using identity (a - b) 2 = a2 +... View Article

Simplify: (t + s²)(t² – s)

Answer: t3 - s3 - st + s2t2 (t + s2) × (t2 - s) =t × (t2 – s)+s2 × (t2 - s) = (t × t2) - (t × s) + (s2... View Article

Simplify: (x + y)(2x + y) + (x + 2y)(x – y)

Answer: 3x2 - y2 + 4xy (x + y) × (2x + y) + (x + 2y) × (x - y) Consider (x + y) × (2x + y) (x + y) × (2x + y) = x... View Article

Simplify: (x + y)(x² – xy + y²)

Answer: x3 + y3 (x + y) × (x2- xy + y2) = x × (x2- xy + y2) + y × (x2- xy + y2) = (x × x2) - (x × xy) + (x... View Article

Simplify: (x² – 5) (x + 5) + 25

Answer: x3 + 5x2 - 5x (x2 - 5) × (x + 5) + 25 = [x2 × (x + 5) - 5(x + 5)] + 25 = [(x2 × x) + (x2 × 5) - (5× x) -... View Article

Small amount of a mineral salt present naturally in water makes it a______________ of electricity.

Answer: A small amount of a mineral salt present naturally in water makes it a conductor of electricity. Electrical conductor is defined as... View Article

Sometimes, a crackling sound is heard while taking off a sweater during winters. Explain.

Answer: Wool, which is a poor conductor of electricity, is used to make sweaters. When we wear the sweater, the wool comes into contact with our... View Article

Soni says that the acceleration in an object could be zero even when several forces are acting on it. Do you agree with her? Why?

Answer: Acceleration is defined as the rate of change of velocity with respect to time. Acceleration is a vector quantity as it has both... View Article

M	T	W	T	F	S	S
			1	2	3	4
5	6	7	8	9	10	11
12	13	14	15	16	17	18
19	20	21	22	23	24	25
26	27	28	29	30	31