Use identities to evaluate: (i) (101)^2

Evalute: (i) (7x/8 + 4y/5)^2

Evaluate: (i) (a/2b + 2b/a)^2 - (a/2b - 2b/a)^2 - 4

If a + b = 7 and ab = 10; find a - b.

If a - b = 7 and ab = 18; find a + b.

If x + y = 7/2 and xy = 5/2; find: (i) x - y

If a - b = 0.9 and ab = 0.36; find: (i) a + b

If a - b = 4 and a + b = 6; find (i) a^2 + b^2

If 3a + 4b = 16 and ab = 4; find the value of 9a^2 + 16b^2.

The number a is 2 more than the number b. If the sum of the squares of a and b is 34, then find the product of a and b.

The difference between two positive numbers is 5 and the sum of their squares is 73. Find the product of these numbers.

Find the cube of: 3a - 2b

Find the cube of: 5a + 3b

Find the cube of: 2a + 1/2a

Find the cube of: 3a – 1/a (a ≠ 0)

If a^2 + 1/a^2 = 47 and a ≠ 0 find: (i) a + 1/a (ii) a^3 + 1/a^3

If a^2 + 1/a^2 = 18; a ≠ 0 find: (i) a - 1/a (ii) a^3 - 1/a^3

If a + 1/a = p and a ≠ 0; then show that: a^3 + 1/a^3 = p(p^2 - 3)

If a + 2b = 5; then show that: a^3 + 8b^3 + 30ab = 125.

If (a + 1/a)^2 = 3 and a ≠ 0, then show: a^3 + 1/a^3 = 0.

If a + 2b + c = 0; then show that: a^3 + 8b^3 + c^3 = 6abc

If a ≠ 0 and a - 1/a = 3; find: (i) a^2 + 1/a^2 (ii) a^3 - 1/a^3

Use property to evaluate: (i) 13^3 + (-8)^3 + (-5)^3 (ii) 7^3 + 3^3 + (-10)^3 (iii) 9^3 - 5^3 - 4^3 (iv) 38^3 + (-26)^3 + (-12)^3

If a ≠ 0 and a - 1/a = 4; find: (i) a^2 + 1/a^2 (ii) a^4 + 1/a^4 (iii) a^3 - 1/a^3

If x ≠ 0 and x + 1/x = 2; then show that: x^2 + 1/x^2 = x^3 + 1/x^3 = x^4 + 1/x^4

If 2x - 3y = 10 and xy = 16; find the value of 8x^3 - 27y^3.

Expand: (3x + 5y + 2z) (3x - 5y + 2z)

The sum of two numbers is 9 and their product is 20. Find the sum of their (i) Squares (ii) Cubes

Two positive numbers x and y are such that x > y. If the difference of these numbers is 5 and their product is 24, find: (i) Sum of these numbers (ii) Difference of their cubes (iii) Sum of their cubes.

Expand: (2x – 1/x) (3x + 2/x)

Expand: (x + y - z)^2

If a + b + c = 12 and a^2 + b^2 + c^2 = 50; find ab + bc + ca.

If a^2 + b^2 + c^2 = 35 and ab + bc + ca = 23; find a + b + c.

If a + b + c = p and ab + bc + ca = q; find a^2 + b^2 + c^2.

If a + b + c = p and ab + bc + ca = q; find a^2 + b^2 + c^2.

If a^2 + b^2 + c^2 = 50 and ab + bc + ca = 47, find a + b + c.

If x + y - z = 4 and x^2 + y^2 + z^2 = 30, then find the value of xy - yz - zx.

If x + 2y + 3z = 0 and x^3 + 4y^3 + 9z^3 = 18xyz; evaluate:

If a + 1/a = m and a ≠ 0; find in terms of 'm'; the value of: (i) a - 1/a (ii) a^2 - 1/a^2

In the expansion of (2x^2 - 8) (x - 4)^2; find the value of (i) coefficient of x^3 (ii) coefficient of x^2 (iii) constant term

If x > 0 and x^2 + 1/9x^2 = 25/36. Find: x^3 + 1/27x^3

If 2(x^2 + 1) = 5x, find: (i) x - 1/x (ii) x^3 - 1/x^3

If a^2 + b^2 = 34 and ab = 12; find: (i) 3(a + b)^2 + 5(a - b)^2 (ii) 7(a - b)^2 - 2(a + b)^2

If 3x - 4/x = 4 and x ≠ 0; find: 27x^3 - 64/x^3.

If x^2 + 1/x^2 = 7 and x ≠ 0; find the value of: 7x^3 + 8x - 7/x^3 - 8/x.