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yuka

数1の展開

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3 次の式を展開せよ。
(1) (a²-2bc)(bc+3a²)
*(3) (x−y)²(x+y)²(x² + y²)²
(5) (x²+xy+y²)(x² −xy+y²)
(7) (3x-y+1)(2x+y-1)
(2) (m²-2m-1)²
*(4) (a+b-c-d)(a-b-c+d)
*(6) (k+2)(k-1) (k²-k+2)
(8) (2a-2b+c)(a-b-c)

(2式) -y+3)+-y+7
別解
-2x²-2x-x+3x²+9y
= 2x²7x+xy-3+8y+3
(与式)=2x+5-32x2(x2+5_3x)
21 (1) (5=(2x+(a=11²
4+5-3.x)
3x³ +15x9x²-2x¹10x² +6x³
=-2x+9x3-2327x20
x) = (2x) + a²+(-1)²
+-y+3)
22の頃は
+x-x
= (2x)²2-2x (a-1a-1)²
= 4x²a-4)x+ 2a + 1)
+2-2x a+2.1)+2..(2x)
=4²+ a² +1+x-2a-
=4²+(4a-x+(a²-201)
(2 (5)=a-2a-2-3+(ax-2-2).(-)
3ax-6a-6-ax² +20+2x
x 3xxx(-x²)-3x³-
-ax² +50+2)x+6)
よって,xの係数は
4x²-20+ 12x
=2x3
2
23 (1) (t)=(a²-2bc)(3a² + bc)
(2) (与式)={(m² -2m-1}2
= 1·3(a ²)² + (1-bc+(-2bc)-3a²
+(-2bc). bc
= 3a4-5a²bc-2b²c²
= (m²-2m)² -2.(m²-2m) 1+1²
= (m²)²-2.m².2m +(2m)²
-2m² +4m +1.,
=m¹-4m³ +4m² -2m² + 4m+i
=m¹-4m³ +2m² +4m +1
SU (5x) = (m²)² + (−2m)² + (−1)²
+2 m².(-2m) +2.(-2m) (-1)
+2.(-1).m²
=m¹ +4m² +1-4m³ +4m-2m²
=m¹-4m³ +2m² +4m+1
(3) (5x) = {(x−y)(x+y)}² ×(x² + y²)²
= (x² - y²)²(x² + y²) ²
= {(x² - y²)(x² + y²)}²
= {(x²)²-(y²)²²
= (x² - y¹)²
= (x¹)²-2-x²-y¹ + (y¹)²
=x²-2x¹v¹ + po
(4) (5x)=((a−c)+(b-d)||(a-c)-(b-d))
=(a-c)²-(b-d)²
=a²-2ac+c² − (b² − 2bd+d²)
=a²-b² +c²-d²-2ac+2bd
(5) (5x) = {(x² + y²) + xy}{(x² + y²) − xy)
= (x² + y²)²-(xy)²
= ((x²)² +2+x²- y² + (y²)²) — x²y²
= (x¹+2x²y² + y²¹)-x²y²
= x² + x²y² + y²
(6) (与式)=(k+2)(k-1)×(k²-k+2)
=(k²+k-2)(k-k+2)
= (k² + (k − 2)}{k²—(k-2)]
=(k2)²-(k-2²
= k¹-(k²-4k+4)
= k¹-k² +4k-4
(7) (与式) = (3x-(y-1)}{2x+(y-1))
=3.2x2+(3.(y-1)-(y-1) ・2)x-(y-1)2
=6x²+(y-1)x-(y2-2y+1)
=6x2+xy-x-y2+2y-1
=6x2+xy-y2-x+2y-1
(8) (与式) = 12(a-b+c)(a-b)-c)
= 2.1 (a−b)²+(2-(-c)+c-1} (a - b)
+c. (c)
=2(a²-2ab+b²)-c(a−b)-c²
=2a²-4ab+26²-ac+bc-c²
= 2² +26²-c²-4ab+bc-ca
24 (1) (x)= x(x+3)x(x+1)(x+2)
3x)(x² + 2)
x²+3x+3x)+2)
=x2+3+2(x2+3
=x+x³ +9x² +
+6x
+6x³+1 +6x
(2与式) (+1)(x-4) X-1)(x-2)
(x²-3x4x²-3x+2
= [(x²-3-4}{(x² - 2x==2}
=x²-3x)²-2(x²)-8
-5
4-6x³+9 2x²+6x-8
=x¹-6x³-7²+6x-8
(3)-¹)=(x+2x2)x(x+5)(-5)
=(x-4)(x²-25)
数学Ⅰ
TRIAL A'B'

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