Factorisation
练习14.1
问题1:求给定项的公因式。
(i) 12x, 36
答:“12 x = 2 xx2xx3xx \”
“36 = 2 xx2xx3xx3”
这里，公因数' = 2xx3=6 '
(ii) 2y, 22xy
答:“2 y = 2 xx \ y”
“22 y = 2 xx11xx \ y”
公因数= 2
(iii) 14 pq, 28 p2问2
答:“14 pq = 2 xx7xx \ p \ xx \ '
“28 p ^ 2 ^ 2 = 2 xx2xx7xx \ p \ xx \ \ xx \ \ xx \ q '
公因数' =2xx7xx\p\xx\q '
(iv) 2x, 3x²，4
答:“2 x = 2 xx \ x”
' 3 x ^ 2 = 3 xx \ \ xx \ x '
“4 = 2 xx2”
公因数= 1
除了单位没有公因数，所以公因数= 1
(v) 6abc 24ab²12a²b
答:“6 abc = 2 xx3xx \ \ xx \ b \ xx \ c '
《24 ab ^ 2 = 2 xx2xx2xx3xx \ \ xx \ b \ xx \ b”
' 12 a ^ 2 = 2 xx2xx3xx \ \ xx \ \ xx \ b”
公因式' =2xx3xx\a\xx\b '
(vi) 16 x³，- 4x²，32x
答:' 16 x ^ 3 = 2 xx2xx2xx2xx \ \ xx \ \ xx \“
' 4 x ^ 2 = 2 xx2xx \ \ xx \ x '
“32 x = 2 xx2xx2xx2xx2xx \”
公因式' =2x '
(vii) 10 pq, 20qr, 30rp
答:“10 pq = 2 xx5xx \ p \ xx \ '
20 qr = 2 q xx2xx4xx \ \ xx \ r '
30卢比= 2 xx3xx5xx \ r \ xx \ p '
公因数' =2xx5=10 '
(viii) 3x²y³10x³y²6x²y²z
答:' 3 x ^ 2 y ^ 3 = 3 xx \ x \ xx \ \ xx \ \ xx \ y \ xx \ y '
“10 x ^ 3 y ^ 2 = 2 xx5xx \ x \ xx \ \ xx \ x \ xx \ \ xx \ y '
“x ^ 2 y ^ 2 z y = x \ xx \ \ xx \ \ xxy \ xx \ z”
共同因素= x ^ 2 y ^ 2的
问题2:分解下列表达式。
(i) 7x - 42
答:“7 x-42”
' = 7 xx \ x-7xx6 = 7 (x6) '
(ii) 6p - 12q
答:“6 p-12q”
' = 6 xx \ p-6xx2q = 6 (p-2q) '
(iii) 7a²+ 14a
答:7 ^ 2 + 14的
' = 7 xx \ \ xx \ + 7 xx2xx \ = 7(+ 2)”
(iv) - 16z + 20z³
答:-16 z + 20 z ^ 3
' = 4 xx4xx \ z + 4 xx5xx \ z \ xx \ z \ xx \ z '
' = 4 z (4 + 5 z \ xx \ z) = 4 z z ^ 2 - 4 (5)
(v) 20l²m + 30a l m
答:“20 l ^ 2 m + 30 alm”
l l ' = 2 xx2xx5xx \ \ xx \ \ xx \ m + 2 xx3xx5xx \ \ xx \ l \ xx \ m”
' = 2 lm (10 l + 15)
(vi) 5x²y - 15xy²
答:“5 x ^ 2 y-15xy ^ 2》
' = 5 xx \ x \ xx \ \ xx \ y-3xx5xx \ x \ xx \ \ xx \ y '
' = 5 x (xy-3y ^ 2)”
(vii) 10a²- 15b²+ 20 c²
答:“10 ^ 2-15b ^ 2 + 20 c ^ 2
' = 2 xx5xx \ \ xx \ a-3xx5xx \ b \ xx \ b + 4 xx5xx \ \ xx \ c '
' = 5 (2 ^ 2-3b ^ 2 + 4 c ^ 2)”
(viii) - 4a²+ 4ab - 4ca
答:“4 a ^ 2 + 4 ab-4ca”
' = 4 xx \ \ xx \ + 4 xx \ \ xx \ b-4xx \ c \ xx \ '
“= 4 (a - b + c)”
(ix) x²y z + x y²z + x y z²
答:“x ^ 2 yz + xy xyz ^ ^ 2 z + 2》
“y = x \ xx \ \ xx \ \ xx \ z + x \ xx \ \ xx \ y \ xx \ z + x \ xx \ \ xx \ z \ xx \ z '
' = xyz (x + y + z)”
(x) a x²y + b x y²+ c x y z²
答:“ax ^ yz + bxy ^ 2 z + cxyz ^ 2”
' = x \ xx \ \ xx \ x \ xx \ \ xx \ z + b \ xx \ x y \ xx \ \ xx \ \ xx \ z + c \ xx \ x \ xx \ \ xx \ z \ xx \ z '
' = xyz (ax + by + cz) '
问题3:分解。
(i) x²+ xy + 8x + 8y
答:“x ^ 2 + 8 xy + 8 x + y '
' = x \ xx \ x + y \ xx \ \ x + 8 + 8 xx xx \ y '
' = x (x + y) + 8 (x + y) '
' = (x + 8) (x + y) '
(ii) 15xy - 6x + 5y - 2
答:“15 xy-6x + 5 y 2”
' = 3 xx5xx \ \ xx \ y-2xx3xx \ x + 5 xx \ y 2 '
' = 3 x (5 y 2) + 1 (5 y 2) '
' = x (3 + 1) (5 y 2)”
(iii) ax + bx - ay - by
答:“ax + bx-ay-by”
' = x (a + b) - y (a + b)”
' = (x - y) (a + b) '
(iv) 15 pq + 15 + 9q + 25p
答:“15 q pq + 15 + 9 + 25 p '
' = 5 xx3xx \ pq + 5 xx3 + 3 xx3q + 5 xx5p '
' = 5 xx3pq + 3 xx3q + 5 xx5p + 5 xx3”
' = 3 q (5 p + 3) + 5 (5 p + 3)
' = (3 q + 5) (5 p + 3)
(v) z - 7 + 7xy - xy z
答:“z - 7 + 7 xy-xyz”
' = z-xyz-7 + 7 xy’
' = z (1-xy) 7 (1-xy) '
' = (z - 7) (1-xy) '