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Use the given algebraic expression to complete the table of number patterns.

If the number of digits formed is taken to be n, the number of segments needed to form n digits is given by the algebraic expression appearing... View Article

Simplify the expression and find its value when a = 5 and b = – 3. 2(a² + ab) + 3 – ab

Solution From the given details we get to know that a = 5 and b = -3 We have, = 2a2 + 2ab + 3 – ab = 2a2 + ab + 3 On... View Article

What should be the value of a if the value of 2x² + x – a equals to 5, when x = 0?

Solution From the given details we get to know that x = 0 We have, 2x2 + x – a = 5 a = 2x2 + x – 5 On substituting the value of x in the... View Article

If p = – 10, find the value of p² – 2p – 100

Solution From the given details we get to know that p = -10 We have, = p2 – 2p – 100 On substituting the value of p in the above... View Article

If z = 10, find the value of z² – 3(z – 10).

Solution From the given details we get to know that z = 10 We have, = z3 – 3z + 30 On substituting the value of z in the above... View Article

Simplify these expressions and find their values if x = 3, a = – 1, b = – 2. (i) 3x – 5 – x + 9 (ii) 2 – 8x + 4x + 4 (iii) 3a + 5 – 8a + 1 (iv) 10 – 3b – 4 – 5b (v) 2a – 2b – 4 – 5 + a

Solution (i) 3x – 5 – x + 9 Answer From the question we get to know that x = 3 We have, = 3x – x – 5 + 9 = 2x + 4 On... View Article

Simplify the expressions and find the value if x is equal to 2 (i) x + 7 + 4 (x – 5) (ii) 3 (x + 2) + 5x – 7 (iii) 6x + 5 (x – 2) (iv) 4(2x – 1) + 3x + 11

Solution (i) x + 7 + 4 (x – 5) Answer From the given details we get to know that x = 2 We have, = x + 7 + 4x – 20 = 5x + 7 – 20... View Article

When a = 0, b = – 1, find the value of the given expressions: (i) 2a + 2b (ii) 2a² + b² + 1 (iii) 2a²b + 2ab² + ab (iv) a² + ab + 2

Solution (i) 2a + 2b Answer From the given details we get to know that a = 0, b = -1 On substituting the values of a and b in the given algebraic... View Article

If a = 2, b = – 2, find the value of: (i) a² + b² (ii) a² + ab + b² (iii) a² – b²

Solution (i) a2 + b2 Answer From the given details we get to know that a = 2, b = -2 On substituting the values of a and b in the given... View Article

Find the value of the following expressions, when x = -1: (i) 2x – 7 (ii) – x + 2 (iii) x² + 2x + 1 (iv) 2x² – x – 2

Solution (i) 2x – 7 Answer From the given details we get to know that x = -1 On substituting the value of x in the given algebraic equation... View Article

If p = – 2, find the value of: (i) 4p + 7 (ii) – 3p2 + 4p + 7 (iii) – 2p² – 3p²+ 4p + 7

Solution From the given details we get to know that p = -2 On substituting the value of p in the given algebraic equation and simplifying we get... View Article

If m = 2, find the value of: (i) m – 2 (ii) 3m – 5 (iii) 9 – 5m (iv) 3m2 – 2m – 7 (v) (5m/2) – 4

Solution (i) m – 2 Answer From the given details we get to know that m = 2 On substituting the value of m in the given algebraic equation... View Article

From the sum of 4 + 3x and 5 – 4x + 2x², subtract the sum of 3x² – 5x and -x² + 2x + 5.

Solution First we need to determine the sum of 4 + 3x and 5 – 4x + 2x2 = 4 + 3x + (5 – 4x + 2x2) = 4 + 3x + 5 – 4x +... View Article

From the sum of 3x – y + 11 and – y – 11, subtract 3x – y – 11.

Answer: First, we need to determine the sum of algebraic expression 3x – y + 11 and – y – 11 = 3x – y + 11 + (-y – 11) = 3x – y + 11 – y –... View Article

What should be taken away from 3x² – 4y² + 5xy + 20 to obtain – x² – y² + 6xy + 20?

Solution Let us assume S be the required term Then, 3x2 – 4y2 + 5xy + 20 – S = -x2 – y2 + 6xy + 20 S = 3x2 – 4y2 + 5xy + 20 – (-x2 – y2 +... View Article

What should be subtracted from 2a + 8b + 10 to get – 3a + 7b + 16?

Solution Let us assume S be the required term Then, 2a + 8b + 10 – S = -3a + 7b + 16 S = (2a + 8b + 10) – (-3a + 7b + 16) S = 2a... View Article

What should be added to x² + xy + y² to obtain 2x² + 3xy?

Solution Let us assume S be the required term Then, S + (x2 + xy + y2) = 2x2 + 3xy S = (2x2 + 3xy) – (x2 + xy + y2)... View Article

Subtract: 4pq – 5q² – 3p² from 5p² + 3q² – pq

4pq – 5q2 – 3p2 from 5p2 + 3q2 – pq Answer On combining the like terms and subtracting them we get =... View Article

Subtract: 5a² – 7ab + 5b² from 3ab – 2a² – 2b²

5a2 – 7ab + 5b2 from 3ab – 2a2 – 2b2 Answer On combining the like terms and subtracting them we get = 3ab... View Article

Subtract: – x² + 10x – 5 from 5x – 10

– x2 + 10x – 5 from 5x – 10 Answer On combining the like terms and subtracting them we get = 5x – 10 –... View Article

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