Đáp án+Giải thích các bước giải:
Bài 1:
a) 3x².(7xy²-4x-3y²-5)
= 3x².7xy²-3x².4x+3x².3y²-3x².5
= 21x³y²-12x³+9x²y²-15x²
b) -4/5xy.(7x²-3/4y+5)
= (-4/5xy).7x²+(-4/5xy).(-3/4y)+(-4/5xy).5
= -28/5x³y+3/5xy²-4xy
c) (2x-5).(3x²-7x-4)
= 2x.(3x²-7x-4)-5.(3x²-7x-4)
= 6x³-14x²-8x-15x²+35x+20
= 6x³-(14x²+15x²)+(35x-8x)+20
= 6x³-19x²+27x+20
d) (-2x²-5x+3).(7-4x)
= 7.(-2x²-5x+3)-4x.(-2x²-5x+3)
= -14x²-35x+21+8x³+20x²-12x
= 8x³+(20x²-14x²)-(35x+12x)+21
= 8x³+6x²-47x+21
Áp dụng Tổng quát: A.(B+D)=A.B+A.D= AB+AD
Bài 2:
a) (2x+5)² = (2x)²+2.2x.5+5²
= 4x²+20x+25
b) (7x-3)² = (7x)²-2.7x.3+3²
= 49x²-42x+9
c) (3x+2)³ = (3x)³+3.(3x)².2+3.3x.2²+2³
= 27x³+54x²+36x+8
d) (2x-3y)³= (2x)³-3.(2x)².3y+3.2x.(3y)²-(3y)³
= 8x³-36x²y+54xy²-27y³
Áp dụng hằng đẳng thức:
(A+B)²=A²+2AB+B²
(A-B)²=A²-2AB+B²
A²-B²=(A+B).(A-B)
(A+B)³=A³+3A²B+3AB²+B³
(A-B)³=A³-3A²B+3AB²-B³
Bài 3:
a) x²+2x+1 = x²+2.x.1+1²
= (x+1)²
b) x²-6x+9 = x²-2.x.3+3²
= (x-3)²
c) 4x²-y² = (2x)²-y²
= (2x+y).(2x-y)
d) x³+3x²-3x+1= x³+3.x².1+3.x.1²+1³
= (x+1)³
e) 8x³-21x²+6x-1 = (2x)³-3.(2x)².1+3.2x.1²-1³
= (2x-1)³
CHÚC BẠN HỌC TỐT!!!
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