Đáp án:

Giải thích các bước giải:

$\text{Bài 1:}$

$\text{a) ( 3xy² - 5x)²}$

$\text{= $9x²y^{4}$ - 30x²y² + 25x²}$

$\text{b) ( $\frac{1}{2}$x + 5y)² }$

$\text{= $\frac{1}{4}$x² + 5xy + 25y² }$

$\text{c) (-x + 10)²}$

$\text{= x² - 20x + 100}$

$\text{d) (-3x + 7)²}$

$\text{= 9x² - 42x + 49}$

$\text{e) 100x² - 81y²}$

$\text{= (10x - 9y)(100x + 9y)}$

$\text{f) (-2x - 7)²}$

$\text{= 4x² + 28x +49}$

$\text{Bài 2:}$

$\text{a) (2x-3)² = 4x² - 12x + 9}$

$\text{b) ($\frac{1}{5}$x + 6xy²)² = $\frac{1}{25}$x² +  $\frac{12}{5}$x²y² + 36x²$y^{4}$ }$

$\text{c) (4x - 3y)(4x + 3y) = 16x² - 9y²}$

$\text{d) (5x + 8)(5x - 8)= 25x² - 64}$

$\text{e) (3x - 1)² = 9x² - 6x +1}$

$\text{f) (4x - 2)²= 16x² - 16x +4}$

$\text{Bài 3:}$

$\text{a) A= (4x-2)(4x+2)+(2x+5)²-x(x+1)}$

$\text{A= 16x²-4+4x²+20x+25-x²-x}$

$\text{A= 19x²+19x+21}$

$\text{Với x=2 thì:}$

$\text{A = 19.2²+19.2+21}$

$\text{A= 19.4+19.2+21}$

$\text{A= 135}$

$\text{Vậy A= 135 với x=2}$

$\text{b) B= (3-2x)²+(x+1)²-11(2x+5)(2x-5)}$

$\text{B= 9 -12x+4x²+x²+2x+1-11(4x²-25)}$

$\text{B= 9-12x+4x²+x²+2x+1-44x²+275}$

$\text{B= -39x²-10x+285}$

$\text{Với x= 3 thì :}$

$\text{B= -39.3²-10.3+285}$

$\text{B= -39.9-10.3+285}$

$\text{B= -96}$

$\text{Vậy B= -96 với x=3}$

$\text{c) C= (-x+5)²+(3x-1)²+(-7x+1)²}$

$\text{C= x²-10x+25+9x²-6x+1+49x²-14x+1}$

$\text{C= 59x²-30x+27}$

$\text{Với x=-2 thì:}$

$\text{C= 59.(-2)²-30.(-2)+27}$

$\text{C= 59.4+30.2+27}$

$\text{C= 323}$

$\text{Vậy C=323 với x=-2}$