\(\left(100^2+98^2+...+2^2\right)-\left(99^2+97^2+...+1^2\right)\)

\(=\left(100^2-99^2\right)+\left(98^2-97^2\right)+....+\left(2^2-1^2\right)\)

\(=\left(100-99\right)\left(100+99\right)+\left(98-97\right)\left(98+97\right)+...+\left(2-1\right)\left(2+1\right)\)

\(=100+99+98+97+....+2+1=5050\)

bai1 

\(3a\left(2+b\right)-a\left(1-b\right)-4ab=6a+3ab-a+ab-4ab=5a=\frac{5}{229}\)

bai3

\(M=4\left(X-6\right)-x^2\left(2+3x\right)+x\left(5x-4\right)+3x^2\left(x-1\right)=\)

\(4x-24-2x^2-3x^3+5x^2-4x+3x^3-3x=-24\)

bai 4

\(\text{a(x-y)+b(y-x)}=\left(x-y\right)\left(a-b\right)\)

bai 5

ta co cong thuc tinh tong 1+2+3+4+5+...+150=\(\frac{\left(1+150\right)150}{2}=11325\)

a¹¹³²⁵

bai 6

\(p=x\left(5x+15y\right)-5y\left(3x-2y\right)-5y^2+10\)

\(=5x^2+15xy-15xy+10y^2-5y^2+10=5x^2+5y^2+10=5\left(x^2+y^2\right)+10\)

ta nhan thay rang de P=10  thi (x²+y²)=0 suy ra x=y=0 

                                  P=0 thi (x²+y²)=  -2  ma so chinh phuong bao gioi cung lon hon 0 nen truong hop nay vo nghiem de thoa man

\(4x^2+4xy+y^2\)

\(=\left(2x\right)^2+2.2x.y+y^2\)

\(=\left(2x+y\right)^2\)

4x² + 4xy + y²

= (2x)² + 2.2x.y + y²

= (2x+y)²

chị mua sách giải về tham khảo nha!

chúc chị hok tốt!

\(A=x^5-70x^4-70x^3-70x^2-70x+34\)

\(\Rightarrow A=x^5-\left(x-1\right)x^4-\left(x-1\right)x^3-\left(x-1\right)x^2-\left(x-1\right)x+34\)

\(A=x^5-x^5+x^4-x^4+x^3-x^3+x^2-x^2+x+34\)

\(A=71+34\)

\(A=105\)

Nhân ra được a²+b²+c²=2ab+2ac+2bc

=>(a+b+c)^2=4ab+4ac+4bc

=>36=4M

=>M=9

a² + b² + c² = ( a - b )² + ( b - c )² + ( a - c )²

=> a² + b² + c² = a² - 2ab + b² + b² - 2bc - c² + a² - 2ac +c²

=> a² + b² + c² = 2ab + 2bc + 2ac

Có :  a + b + c = 6

=> ( a + b + c )² = 6²

=> a² + b² + c² + 2ab + 2bc + 2ac = 36

Mà a² + b² + c² = 2ab + 2bc + 2ac

=> 2ab +  2ac + 2bc + 2ab + 2ac + 2bc = 36

=> 4ab + 4ac + 4bc = 36

=> ab + ac + bc = 9

Mà M = ab + ac + bc

Vậy M = 9

e 6x\(6x^2-12x-5x^2+10x=x^2-2x\)

thay x\(x=2\)  vào \(x^2-2x\)  ta có\(2^2-2\times2=4-4=0\)0

x(x-y)+y(x+y)

=x^2-xy+xy+y^2

=x^2+y^2

X[X - Y] + Y[X + Y]

= x²-xy+xy+y²

= x²+y²

X[X² - Y] - X² [X + Y] + Y[X² - Y]

=x³-xy-x³ -x²y+ x²y-y²

= -xy-y²

 ~ chúc bạn học tốt ~

\(A=-3x\left(x-5\right)+3\left(x^2-4x\right)-3x+10\)

\(A=-3x^2+15x+3x^2-12x-3x+10\)

\(A=10\)

\(B=4\left(x-6\right)-x^2\left(2+3x\right)+x\left(5x-4\right)+3x^2\left(x-1\right)\)

\(B=4x-24-2x^2-3x^3+5x^2-4x+3x^3-3x^2\)

\(B=-24\)

-2x^3y+5/2x^2y^2-x^2y

GIẢI RA LUÔN ĐI BN