Chapter 3 Brackets and Operations with Them

Example 3_1 pgno:42

In [3]:
#simplify a(a^2+ab+b^2)

print('a^3+(a^2)b+a(b^2)')

a^3+(a^2)b+a(b^2)

Example 3_2 pgno:42

In [4]:
#simplify 2(4a+3b)+6(2a-b)

#b gets cancelled  
print('20a')

20a

Example 3_3 pgno:42

In [5]:
#simplify 5x-(5y+2x)

#on adding like terms
print('3x-5y')

3x-5y

Example 3_4 pgno:43

In [6]:
#simplify 3(4a-b)-2(3a-2b)

#by removing braces
a_coeff=3*4-2*3;b_coeff=-3-2*-2;
print"total=a+b\n",a_coeff,b_coeff

total=a+b
6 1

Example 3_5 pgno:43

In [7]:
#x(2x-y)-x(x-y)-y(x+2y)

#("1)after simplifying")
print('x^2-x*y-2*y^2')
print("2)after substituting given values")
x=2;y=1;
val=x^2-x*y-2*y^2;
print val

x^2-x*y-2*y^2
2)after substituting given values
-2

Example 3_6 pgno:45

In [8]:
#simplify 2(3a+5(b+c))

#by removing braces,
print('6a+10b+10c')

6a+10b+10c

Example 3_7 pgno:45

In [9]:
#simplify 3(3a-2(a-b))

#by removing braces,
a_coeff=3*3-3*2;b_coeff=3*2;
print"total=a+b\n",a_coeff,b_coeff

total=a+b
3 6

Example 3_8 pgno:45

In [10]:
#simplify 12a-2[3a-(4-2(a-3))]

#a is a polynomial function with degree zero

print "12*a-2*[3*a-{4-2*(a-3)}]"
print '20*a+20'

12*a-2*[3*a-{4-2*(a-3)}]
20*a+20