1.Write the equation for the following expressions
(a) x is multiplied by itself and then added to the product of x and y .
(b) Three times of p and two times of q are multiplied and then subtracted from r .
(c) Product of p , twice of q and thrice of r .
(d) Sum of the products of a and b , b and c and c and a.
(e) Perimeter of an equilateral triangle of side x.
(f) Perimeter of a rectangle with length p and breadth q .
(g) Area of a triangle with base m and height n .
(h) Area of a square with side x.
(i) Cube of s subtracted from cube of t.
(j) Quotient of x and 15 multiplied by x.
(k) The sum of square of x and cube of z .
(l) Two times q subtracted from cube of q .
2.Simplify combining like terms:
(i) 21 b – 32 + 7 b – 20 b
(ii) – z 2 + 13 z 2 – 5 z + 7 z 3 – 15 z
(iii) p – ( p – q ) – q – ( q – p )
(iv) 3 a – 2 b – ab – ( a – b + ab ) + 3 ab + b – a
3.Add:
(i) 3 mn , – 5 mn , 8 mn , – 4 mn
(ii) t – 8 tz , 3 tz – z , z – t
(iii) – 7 mn + 5, 12 mn + 2, 9 mn – 8, – 2 mn – 3
(iv) a + b – 3, b – a + 3, a – b + 3
(v) 14 x + 10 y – 12 xy – 13, 18 – 7 x – 10 y + 8 xy , 4 xy
(vi) 5 m – 7 n , 3 n – 4 m + 2, 2 m – 3 mn – 5
4.If
a
= 2,
b
= – 2, find the value of:(a) x is multiplied by itself and then added to the product of x and y .
(b) Three times of p and two times of q are multiplied and then subtracted from r .
(c) Product of p , twice of q and thrice of r .
(d) Sum of the products of a and b , b and c and c and a.
(e) Perimeter of an equilateral triangle of side x.
(f) Perimeter of a rectangle with length p and breadth q .
(g) Area of a triangle with base m and height n .
(h) Area of a square with side x.
(i) Cube of s subtracted from cube of t.
(j) Quotient of x and 15 multiplied by x.
(k) The sum of square of x and cube of z .
(l) Two times q subtracted from cube of q .
2.Simplify combining like terms:
(i) 21 b – 32 + 7 b – 20 b
(ii) – z 2 + 13 z 2 – 5 z + 7 z 3 – 15 z
(iii) p – ( p – q ) – q – ( q – p )
(iv) 3 a – 2 b – ab – ( a – b + ab ) + 3 ab + b – a
3.Add:
(i) 3 mn , – 5 mn , 8 mn , – 4 mn
(ii) t – 8 tz , 3 tz – z , z – t
(iii) – 7 mn + 5, 12 mn + 2, 9 mn – 8, – 2 mn – 3
(iv) a + b – 3, b – a + 3, a – b + 3
(v) 14 x + 10 y – 12 xy – 13, 18 – 7 x – 10 y + 8 xy , 4 xy
(vi) 5 m – 7 n , 3 n – 4 m + 2, 2 m – 3 mn – 5
(i) a 2 + b 2
(ii) a 2 + ab + b 2
(iii) a 2 – 2 b
(i) 3 x – 5 – x + 9
(ii) 2 – 8 x + 4 x + 4
(iii) 3 a + 5 – 8 a + 1
(iv) 10 – 3 b – 4 – 5 b
(v) 2 a – 2 b – 4 – 5 + a
6.Simplify the expressions and find the value if x is equal to 2
(i) x + 7 + 4 ( x – 5)
(ii) 3 ( x + 2) + 5 x – 7
(iii) 6 x + 5 ( x – 2)
(iv) 4(2 x – 1) + 3 x + 11
7.Solve the following equations:
(a) 2( x + 4) = 12
(b) 3( n – 5) = 21
(c) 3( n – 5) = – 21
(d) – 4(2 + x ) = 8
(e) 4(2 – x ) = 8
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