Đáp án:
Giải thích các bước giải:
1.
a) (x - 1)( 3 - 2x) - 2x ³ ( 2 - x)
= 3x-2x²-3+2x -4x³+$2x^{4}$
=$2x^{4}$ - 4x³ -2x² +5x
b, ( 2x - 1) ² + ( 2x + 1) ² - ( 2x + 1)( 2x - 1)
= ( 2x + 1)( 2x - 1). ( 2x-1 +2x+1 -1)
= ( 4x² -1). (4x -1)
c) 2x(x ² - y + 1) - ( 2x - 1)(x ² + x)
= 2x³ - 2xy +2x -( 2x³ + 2x² + 2x³ -x)
= 2x³ - 2xy + 2x - 4x³ - 2x² +x
= - 2x³ - 2xy - 2x² +x
d) ( 1 + 3x)( 1 - 3x) + 3(x + 1) ²
= 1- 9x² + 3 ( x² +2x +1)
= 1 - 9x² +3x² +6x +3
= - 6x² +6x +4
2.
a) x( 3x -1 ) - ( 3x + 2)(x - 4) = 0
⇔ 3x² - x - ( 3x² - 12x +2x -8) =0
⇔ 3x² - x - 3x² +10x +8 =0
⇔9x + 8=0
⇔ x= $\frac{-8}{9}$
b) ( x + 4 ) ² - x(1 - x) + 2(x - 3)(3 + x) = 0
⇔ x² + 8x +16 - x +x² + 2.( 3x +x² -9 -3x) =0
⇔ 2x² + 7x +16 + 6x +2x² -18 -6x =0
⇔4x² +7x -2 =0
⇔ ( x- $\frac{1}{4}$ ) . ( x+2) =0
⇔ \(\left[ \begin{array}{l}x=\frac{1}{4} \\x=-2\end{array} \right.\)
c) 4x(x + 5) - 3x - 15 = 0
⇔ 4x² + 20x - 3x -15=0
⇔ 4x² -17x -15 =0
⇔ ( x-5). (x+ $\frac{3}{4}$ )=0
⇔\(\left[ \begin{array}{l}x=5\\x=-\frac{3}{4}\end{array} \right.\)
d) ( 4x + 1)3x - ( 3x + 1)( 4x + 3) = 0
⇔ 12x² + 3x - ( 12x² + 9x + 4x +3) =0
⇔ 12x² +3x - 12x² -13x -3=0
⇔-10x - 3=0
⇔-10x = 3
⇔ x= $\frac{-3}{10}$
e) (x + 1)( 1 - 4x) + ( 1 - 2x) ² = 2x - 11
⇔ x - 4x² +1 -4x + 1 - 4x + 4x² - 2x +11 =0
⇔ -5x + 13=0
⇔ x= $\frac{13}{5}$
3.
a) 2mx ² - 3my + 6m
= m .( x²- 3y +6)
b) x ³y - 4x ²y ² + 4y ³
= xy. ( x² - 4xy + 4y²)
= xy.( x-2y)²
c) 4x ( x + 1) - 8
= 4x² + 4x -8
= 4. ( x² +x-2)
d) x ² - y ² + 8x + 16
= ( x² + 8x+16) -y²
= (x+ 4)² -y²
= ( x+4-y).( x+4+y)
e) 4x ² - 9 + (2x + 3) ²
= 4x² -9 + 4x² + 12x + 9
= 12x
f) 2x ² - 4xy + 8x
= ( 2x² + 8x) -4xy
= 2x( x+4) - 4xy
= ( x+4). ( 2x-1).y
