1
1
1− 1 2
1
618. а) x − 2 x 2 = x 2 ( x 1
1
1− 1 3
1−1
б) y + 3 y 3 = y 3 ( y 1
1
1
1
1−1 4
1
1−1 6
1 −1 4)
1
1
5
2
2
− 5a 4
1−1 6)
г) a 3 + a 6 = a 6 (a 3 3
1
2
+ 3 y 3 3 ) = y 3 ( y 3 + 3) .
в) a 2 − 5a 4 = a 4 (a 2 1
1
− 2) = x 2 ( x 2 − 2) .
1
+ a6
3−1 4
5−2 3
− 2b 4
2−2 3)
е) c 3 + 6c 3 = c 3 (c 3
1
1
1
1
= b 4 (b 2 − 2) . 2
= c 3 ( c + 6) .
+ 6c 3 1
1
= a 6 (a 6 + 1) .
1−1 4)
д) b 4 − 2b 4 = b 4 (b 4
1
= a 4 (a 4 − 5) .
1
1
1
⎛ ⎝
1
1
⎞ ⎠
ж) (ab )3 − (ac )3 = a 3 b 3 − a 3 c 3 = a 3 ⎜ b 3 − c 3 ⎟ . 1
1
1 1 1 1 1 1 1 1−1 1 1 ⎛ 1 1−1 ⎞ ⎛ 1 ⎞ з) 6 2 − 2 2 = ( 3 ⋅ 2 ) 2 − 2 2 = 3 2 ⋅ 2 2 − 2 2 = 2 2 ⎜ 3 2 ⋅ 2 2 2 − 2 2 2 ⎟ = 2 2 ⎜ 3 2 − 1⎟ . ⎝ ⎠ ⎝ ⎠
1
1
1− 1 2
619. а) 2 + 2 2 = 2 2 (2 1
1
1− 1 2
б) 3 − 3 2 = 3 2 (3 1
1
1−1 2)
− 32
1− 1 2
1
1
1−1 3
1
1
+ a2
1− 1 3)
−b
1
1
1
= 2 2 (2 2 + 1) . 1
= 3 2 (3 2 − 1) .
1−1 2)
в) a + a 2 = a 2 (a
г) b 3 − b = b 3 (b 3
1 −1 2)
+ 22
1
1
= a 2 (a 2 + 1) . 1
2
= b 3 (1 − b 3 ) .
1
1
1
1
1
1
1
1
1
д) 15 3 + 20 3 = ( 5 ⋅ 3) 3 + ( 5 ⋅ 4 ) 3 = 5 3 ⋅ 33 + 5 3 ⋅ 4 3 = 5 3 (33 + 4 3 ) . 1
1
1
1
1
⎛ ⎝
1
1
⎞ ⎠
е) (2a ) 2 − (5a ) 2 = 2 2 a 2 − 5 2 a 2 = a 2 ⎜ 2 2 − 5 2 ⎟ . 1
1
1
1
1
1
1
2
1
1
620. а) a − b = ( a 2 ) 2 − ( b 2 ) 2 = ( a 2 − b 2 )( a 2 + b 2 ) . 1
1
1
1
1
2
б) a − b = ( a 3 ) 3 − ( b 3 ) 3 = ( a 3 − b 3 )( a 3 + a 3 b 3 + b 3 ) . 1 ⋅2
1
1
1
621. а) m 2 − 5 = m 2 − 5 2 = m 2 − (5 2 ) 2 = (m + 5 2 )(m − 5 2 ) . 1 ⋅2
1
1
1
б) 2 − x 2 = 2 2 − x 2 = (2 2 ) 2 − x 2 = (2 2 + x)(2 2 − x) . 3
3
3
в) a 3 − 4 = (a 2 ) 2 − 22 = (a 2 + 2)(a 2 − 2) . 2
4
1
2
1
2
1
2
г) x 5 − y 5 = ( x 5 ) 2 − ( y 5 ) 2 = ( x 5 + y 5 )( x 5 − y 5 ) . 1
1
1
д) 4 − a = 22 − ( a 2 ) 2 = (2 + a 2 )(2 − a 2 ) . 1 ⋅2
1 ⋅2
1
1
1
1
1
1
е) m − n = ( m 2 − n 2 ) = (m 2 ) 2 − (n 2 ) 2 = (m 2 + n 2 )(m 2 − n 2 ) . 210