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a)49-a2+2ab-b2=49-(a2-2ab+b2)=49-(a-b)2=(7-a+b)(7+a-b)
b)a2-b2+4bc-4c2=a2-(b2-2bc+c2)=a2-(b-2c)2=(a-b+2c)(a+b-2c)
c)4b2c2-(b2+c2-a2)2=(4bc-b2-c2+a2)(4bc+b2+c2-a2)
d)(a+b+c)2+(a+b-c)2-4c2
=(a+b+c)2+(a+b-c-2c)(a+b-c+2c)
=(a+b+c)2+(a+b-3c)(a+b+c)
=(a+b+c)(a+b+c+a+b-3c)
=(a+b+c)(2a+2b-2c)
=2(a+b+c)(a+b-c)
a, 49 -a^2 + 2ab - b^2 = 7^2 - ( a^2 - 2ab + b^2) = 7^2 - (a-b)^2 = ( 7-a+b) ( 7 +a -b)
b, a^2 - b^2 + 4bc - 4c^2 = a^2 - ( b^2 - 4bc + 4c^2) = a^2 - ( b - 2c)^2 = ( a - b + 2c)( a + b -2c)
c, 4.b^2.c^2 - ( b^2 + c^2 - a^2)^2 = ( 2bc)^2 - ( b^2 + c^2 - a^2)^2 = ( 2bc - b^2 - c^2 +a^2 )( 2bc + b^2 + c^2 - a^2)
= ( 2bc - b^2 - c^2 +a^2 ) [ (b + c)^2 - a^2) = ( 2bc - b^2 - c^2 +a^2 ) ( b + c -a)(b + c + a)
d, ( a+b+c)^2 +( a + b - c)^2 - 4c^2 = ( a + b + c)^2 + ( a + b - c - 2c)( a + b - c + 2c) = ( a+b +c)^2 + ( a+b - 3c)(a+b+c)
= ( a+b+c)( a+ b+ c + a + b - 3c) = ( a+b+c )( 2a + 2b - 2c) = 2(a+b+c)(a+b-c)
bn chép lại đề nhé
a/ \(=\left(x+y\right)^2-4x^2y^2=\left(x+y+2xy\right)\left(x+y-2xy\right)\)
b/ \(=\left(2bc+b^2+c^2-a^2\right)\left(2bc-b^2-c^2+a^2\right)\)
\(=\left[\left(b+c\right)^2-a^2\right]\left[-\left(b+c\right)^2+a^2\right]\)
\(=\left(b+c-a\right)\left(b+c+a\right)^2\left(a-b-c\right)\)
c/ \(=2a^2+2b^2-2c^2+4ab=2\left[\left(a^2+b^2+2ab\right)-c^2\right]\)
\(=2\left(a+b-c\right)\left(a+b+c\right)\)
d/ \(=\left(4x^2-25\right)^2-9\left(4x^2-20x+25\right)\)
\(=\left(4x^2-25\right)^2-9\left(4x^2+25\right)+180x\)
tới đây bạn đặt a= 4x^2 -25 rồi làm típ nha, mình lười quá ><
e/ tương tự câu d nha bạn
f/ \(=a^4\left(a^2-1\right)+2a^2\left(a+1\right)\)
\(=a^4\left(a-1\right)\left(a+1\right)+2a^2\left(a+1\right)\)
\(=a^2\left(a+1\right)\left(a^2+2\right)\)
g/ đặt \(a=3x^2+3x+2\) khi đó biểu thức trở thành
\(a^2-\left(a+4\right)^2=a^2-a^2-8a-16\)
\(=-8a-16=-8\left(3x^2+3x+2-8\right)=-8\left(3x^2+3x-6\right)\)
\(=-24\left(x^2+x-2\right)=-24\left(x-1\right)\left(x+2\right)\)
xong rùi nha bn. Chúc bn hc tốt (xin lỗi tại có mấy câu mình lười nha)
\(x^2-4x^2y^2+y^2+2xy\)
\(=\left(x^2+2xy+y^2\right)-4x^2y^2\)
\(=\left(x+y\right)^2-4x^2y^2\)
\(=\left(x-2xy+y\right)\left(x+2xy+y\right)\)
a) \(x^2-2x+1-y^2=\left(x-1\right)^2-y^2=\left(x-1-y\right)\left(x-1+y\right)\)
b)\(=\left(x+y\right)^2-z^2=\left(x+y+z\right)\left(x+y-z\right)\)
mấy ý còn lại tương tự nha
a,\(x^2-y^2+1-2x\)
\(=\left(x-1\right)^2-y^2\)
\(=\left(x-1+y\right)\left(x-1-y\right)\)
\(b,x^2+2xy-z^2+y^2\)
\(=\left(x+y\right)^2-z^2\)
\(=\left(x+y+z\right)\left(x+y-z\right)\)
a) 16(4x+5)2 - 25(2x+2)2
\(=\left[4\left(4x+5\right)\right]^2-\left[5\left(2x+2\right)\right]^2\)
\(=\left[4\left(4x+5\right)+5\left(2x+2\right)\right]\left[4\left(4x+5\right)-5\left(2x+2\right)\right]\)
\(=\left(16x+20+10x+10\right)\left(16x+20-10x-10\right)\)
\(=\left(26x+30\right)\left(6x+10\right)\)
\(b,\left(x-y+4\right)^2-\left(2x+3y-1\right)^2\)
\(=\left(x-y+4+2x+3y-1\right)\left(x-y+4-2x-2y+1\right)\)
\(=\left(3x+2y+3\right)\left(-x-3y+5\right)\)
\(c,\left(x+1\right)^4-\left(x-1\right)^4\)
\(=\left(x+1\right)^{2^2}-\left(x-1\right)^{2^2}\)
\(=\left[\left(x+1\right)^2+\left(x-1\right)^2\right]\left[\left(x+1\right)^2-\left(x-1\right)^2\right]\)
\(=\left(x^2+2x+1+x^2-2x+1\right)\left[\left(x+1+x-1\right)\left(x+1-x+1\right)\right]\)
\(=\left(2x^2+2\right)2x.2\)
\(=4x.2\left(x^2+1\right)\)
\(=8x\left(x^2+1\right)\)
d,=(2bc+b2+c2−a2)(2bc−b2−c2+a2)
=[(b+c)2−a2][−(b+c)2+a2]
=(b+c−a)(b+c+a)2(a−b−c)
\(a^2-b^2+4bc-4c^2\)
\(=a^2-\left(b^2-4bc+4c^2\right)\)
\(=a^2-\left(b-2c\right)^2\)
\(=\left(a-b+2c\right)\left(a+b-2c\right)\)