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a)\(7x\left(y-4\right)^2-\left(4-y\right)^3=7x\left(4-y\right)^2-\left(4-y\right)^3=\left(4-y\right)^2\left(7x-4+y\right)\)
b)\(\left(4x-8\right)\left(x^2+6\right)-\left(4x-8\right)\left(x+7\right)+9\left(8-4x\right)\)
\(=\left(4x-8\right)\left(x^2+6\right)-\left(4x-8\right)\left(x+7\right)-9\left(4x-8\right)\)
\(=\left(4x-8\right)\left(x^2-x-10\right)=4\left(x-2\right)\left(x^2-x-10\right)\)
a.\(7x.\left(y-4\right)^2-\left(4-y\right)^3\)=\(7x.\left(4-y\right)^2-\left(4-y\right)^3=\left(4-y\right)^2.\left(7x+y-4\right)\)
b.\(\left(4x-8\right).\left(x^2+6\right)-\left(4x-8\right)\left(x+7\right)+9.\left(8-4x\right)\)
=\(\left(4x-8\right)\left(x^2+6-x-7-9\right)=\left(4x-8\right)\left(x^2-x-10\right)\)
Ta có : 5x(x - 2y) + 2(2y - x)2
= 5x(x - 2y) + 2(x - 2y)2 (vì (2y - x)2 = (x - 2y)2 )
= (x - 2y)[5x + 2(x - 2y)]
= (x - 2y)(5x + 2x - 4y)
= (x - 2y)(7x - 4y)
b) 7x(y - 4)2 - (4 - y)3
= 7x(y - 4)2 - (4 - y)2(4 - y)
= 7x(y - 4)2 - (y - 4)2(4 - y)
= (y - 4)2(7x - 4 + y)
c) (4x - 8)(x2 + 6) - (4x - 8)(x + 7) + 9(8 - 4x)
= (4x - 8)(x2 + 6) - (4x - 8)(x + 7) - 9(4x - 8)
= (4x - 8)(x2 + 6 - x - 7 - 9)
= 2(x - 4)(x2 - x - 10)
\(\left(x^2+4x+8\right)^2+3x\left(x^2+4x+8\right)+2x^2=\left(x^2+4x+8+\dfrac{3}{2}x\right)^2-\dfrac{1}{4}x^2=\left(x^2+\dfrac{11}{2}x+8\right)^2-\left(\dfrac{1}{2}x\right)^2=\left(x^2+\dfrac{11}{2}x+8-\dfrac{1}{2}x\right)\left(x^2+\dfrac{11}{2}x+8+\dfrac{1}{2}x\right)=\left(x^2+5x+8\right)\left(x^2+6x+8\right)=\left(x+2\right)\left(x+4\right)\left(x^2+5x+8\right)\)
\(\left(x^2+4x+8\right)^2+3x\left(x^2+4x+8\right)+2x^2\)
\(=\left(x^2+4x+8\right)^2+x\left(x^2+4x+8\right)+2x\left(x^2+4x+8\right)+2x^2\)
\(=\left(x^2+4x+8\right)\left(x^2+5x+8\right)+2x\left(x^2+5x+8\right)\)
\(=\left(x^2+5x+8\right)\left(x+2\right)\left(x+4\right)\)
6, (x^2 +1) -4x^2 = x^2 + 1 - 4x^2 = 1 - (4x^2 - x^2) = 1 - 3x^2 = (1-\(\sqrt{3}\)x)(1+\(\sqrt{3}\)x)
7, x^2 - 4x -5 = x^2 - 2.x.2 + 4 - 9 = (x^2 - 2.x.2 +4) - 3^2 = (x-2)^2 - 3^2 = (x-2-3)(x-2+3) = (x-5)(x+1)
8, x^5 - 3x^4 + 3x^3 - x^2 = x^2(x^3 -3x^2 + 3x -1) = x^2(x-1)^3
Bài 1:
$5x+10=5(x+2)$
Bài 2:
Tại $x=8$ thì $x^2+4x+4=(x+2)^2=(8+2)^2=10^2=100$
Bài 3:
$x^2-6x+9=x^2-2.3.x+3^2=(x-3)^2$
Bài 4:
Diện tích mảnh đất là:
$(x+5)(x-5)=24$
$\Leftrightarrow x^2-25=24$
$\Leftrightarrow x^2=49$
$\Rightarrow x=7$ (do $x>5$)
Chiều dài mảnh đất là: $x+5=7+5=12$ (m)
( 4x - 8 ) . ( x2 + 6 ) - ( 4x - 8 ) . ( x + 7 ) + 9 . ( 8 - 4x )
= (4x - 8 ) . ( x2 + 6 ) - ( 4x - 8 ) . ( x + 7 ) - 9 . (4x - 8)
= (4x-8) ( x2+6 - x - 7 - 9)
= 4(x-2)(x^2 -x - 10)