problem archive
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Factorise: (i) 49a^2 + 70ab + 25b^2 -
Write (3a + 4b + 5c)^2 in expanded form. -
Expand (4a - 2b - 3c)^2 -
Factorise 4x^2 + y^2 + z^2 - 4xy - 2yz + 4xz. -
Write the following cubes in the expanded form: (i) (3a + 4b)^3 (ii) (5p - 3q)^3 -
Evaluate each of the following using suitable identities: (i) (104)^3 (ii) (999)^3 -
Use suitable identities to find the following products: (i) (x+4)(x+10) (ii) (x+8)(x-10) (iii) (3x+4)(3x-5) (iv) (y^3+\frac{3}{2})(y^3-\frac{3}{2}) (v... -
Evaluate the following products without multiplying directly: (i) 103×107 (ii) 95×96 (iii) 104×96 -
Factorise the following using appropriate identities: (i) 9x^2+6xy+y^2 (ii) 4y^2-4y+1 (iii) x^2-\frac{y^2}{100} -
Expand each of the following using suitable identities: (i) (x+2y+4z)^2 (ii) (2x-y+z)^2 (iii) (-2x+3y+2z)^2 (iv) (3a-7b-c)^2 (v) (-2x+5y-3z)^2 (vi) \l... -
Write each of the following equations in the form \(ax + by + c = 0\) and indicate the values of \(a\), \(b\), and \(c\) in each case: (i) \(2x + 3y =... -
Write each of the following as an equation in two variables: (i) y = -5 (ii) y = 2 (iii) 2x = 3 (iv) 5y = 2 -
The cost of a notebook is twice the cost of a pen. Write a linear equation in two variables to represent this statement. -
Express the following linear equations in the form ax + by + c = 0 and indicate the values of a, b and c in each case: (i) 2x + 3y = 9.35 (ii) x - y/5... -
Find four different solutions of the equation x + 2y = 6. -
Find two solutions for each of the following equations: (i) 4x + 3y = 12 (ii) 2x + 5y = 0 (iii) 3y + 4 = 0 -
Which one of the following options is true, and why? y = 3x + 5 has (i) a unique solution, (ii) only two solutions, (iii) infinitely many solutions -
Write four solutions for each of the following equations: (i) 2x + y = 7 (ii) πx + y = 9 (iii) λ = 4y -
Check which of the following are solutions of the equation x - 2y = 4 and which are not: (i) (0, 2) (ii) (2, 0) (iii) (4, 0) (iv) (√2, 4√2) (v) (1, 1) -
Find the value of k if x = 2, y = 1 is a solution of the equation 2x + 3y = k.