Math 017 Materials With Exercises

3(m n)a(x1)g)h)2tx19s s s sThe opposite to is or equivalently , . All students were right.t tt t202a 2a2a2a c (2a c)2a ca) b) b b b 2d2d2d212x 4y2x y 2x 7y3x y 2x 3y 12na)b)c)d)e)f)333 ttk t3(a b) 2( cd 1) ( 2 a ) 3( m n)g)h)txy22 a)x3xx 3x1a b 1 b) 3 c) 3xd) ( a b)y yy y y yy y23 a) 4 a b) 32ac) 2 a d) 64 x e) not possible f) not possible g) 2 x h) 2 xmi) 32j) x2k) xy l) not possible m) 2 x n) 2 x86ybdo) x p) q) 1 x r)5xz 3acs) 0.06xyzt) 4x24 Yes, both are equivalent.25 (x+y)(1+a) and x+y(1+a) are not equivalent. In (x+y)(1+a) the entire expression of (x+y) is multiplied with (1+a) andin x+y(1+a) only y is multiplied with (1+a).26 a) a 2 b c c 2b a b) x x 44 xy 1c) xy4 4aa 2 2e)x y x yab b f) z c c z g) xyz yz( x)h) a 3 3 32 227m m , ,1 1m (1)are equivalent to m.28 m (n)and n m are equivalent to m n :29 a b c d and d b c a are equivalent to a c b d .30 a 1 2aa, a , , are equivalent to a .b b 2b bb31 All of the expressions are equal to32x 4x x, , and2 8 233 8a 3, 3 a 8,345x except656xare equivalent to x 23 8a2 are equivalent to 3 8a21 3ab b 3a1(3a b), ,, and (3a b)are equivalent to66 6 66m n 1 11 n m are equivalent to35m n, m n,( m n) and .3 3 33 33 336 Both John and Mary are right.37 ( )4 4x 1, x 1. Since 1 1 the expressions are not equivalent.2 238 y 53a b .6x , ( x y)2 1, when x 1, y 2 . Since 5 1 the expressions are not equivalent.n ( 1)m 11 m 1, when m 1 b) ( 1)m 1,1 m 1, when m 339 m−n+p=−2, m− (n+p)= −4,when m=2, n=5 5 ,and p=1. Since −2 −4 the expressions are not equivalent.40 a) , m 1 m 1, when m 5 d) ( 1)m 1,1 m 1, when m 7c) ( 1) 1,120Answers to Exercises