http://123link.pro/Hya7

(x+10)(x-2)+x(x²-3)

=x^2 -2x+10x-20+x^3-3x

=x^3+x^2+5x-20

http://123link.pro/37PNwrg

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

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

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

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

http://123link.pro/cS4uABOY

B = 5 - 4x² + 6x 

= -(4x² - 6x - 5)

= -(4x² - 6x + 9/4 - 29/4)

= -(4x² - 6x + 9/4) + 29/4

B = -(2x - 3/2)² + 29/4

Vì -(2x - 3/2)² \(\le0\forall x\)

Nên : B = -(2x - 3/2)² + 29/4 \(\le\frac{29}{4}\forall x\)

Vậy B_max = \(\frac{29}{4}\) khi x = \(\frac{3}{4}\)

chỉnh lại đề: so sánh ..... và    2²⁰⁰

\(\left(2+1\right)\left(2^2+1\right)\left(2^4+1\right)...\left(2^{100}+1\right)\)

\(=\left(2-1\right)\left(2+1\right)\left(2^2+1\right)\left(2^4+1\right)...\left(2^{100}+1\right)\)

\(=\left(2^2-1\right)\left(2^2+1\right)\left(2^4+1\right)...\left(2^{100}+1\right)\)

\(=\left(2^4-1\right)\left(2^4+1\right)...\left(2^{100}+1\right)\)

\(=\left(2^{100}-1\right)\left(2^{100}+1\right)=2^{200}-1< 2^{200}\)

cảm ơn bạn nha mình viết nhầm đề bài

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

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

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

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

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

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

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

4x² + 4xy + y²

= (2x)² + 2.2x.y + y²

= (2x+y)²

chị mua sách giải về tham khảo nha!

chúc chị hok tốt!

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

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

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

\(A=71+34\)

\(A=105\)

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 ~