\(8x^2+18x-5 \)

\(=8x^2-2x+20x-5\)

\(=2x\left(4x-1\right)+5\left(4x-1\right)\)

\(=\left(4x-1\right)\left(2x+5\right)\)

(4x-1)(2x-5)

\(x^2-y^2-2y-1\)

\(=x^2-\left(y^2+2y+1\right)\)

\(=x^2-\left(y+1\right)^2\)

\(=\left(x-y-1\right)\left(x+y+1\right)\)

( x-y-1)

Câu hỏi của Hoàng Thái Dương - Toán lớp 8 - Học toán với OnlineMath

Ta có: \(a-b=7\)

\(\Rightarrow b-a=-7\)

\(B=\frac{3a-b}{2a+7}+\frac{3b-a}{2b-7}\)

\(B=\frac{2a+\left(a-b\right)}{2a+7}+\frac{2b+\left(b-a\right)}{2b-7}\)

\(B=\frac{2a+7}{2a+7}+\frac{2b-7}{2b-7}\)

\(B=1+1\)

\(B=2\)

Vậy \(B=2\)

Tham khảo nhé~

    \(B=\frac{3a-b}{2a+7}+\frac{3b-a}{2b-7}\)

       \(=\frac{2a+\left(a-b\right)}{2a+7}+\frac{2b-\left(a-b\right)}{2b-7}\)

       \(=\frac{2a+7}{2a+7}+\frac{2b-7}{2b-7}\) (vì a - b = 7)

       \(=1+1=2\)

Câu 2 :

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

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

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

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

\(123456^2-123457.1234555\)

\(=123456^2-\left(123456+1\right).\left(123456-1\right)\)

\(=123456^2-123456^2+1^2\)

\(=1\)

Tham khảo nhé~

       \(x^4+6x^2y+9y^2-1\)

\(=\left(x^2\right)^2+2.x^2.3y+\left(3y\right)^2-1\)

\(=\left(x^2+3y\right)^2-1\)

\(=\left(x^2+3y-1\right)\left(x^2+3y+1\right)\)

Chúc bạn học tốt.

\(\left(x^2+4x-3\right)^2-5x.\left(x^2+4x-3\right)+6x^2\)

\(=\left[\left(x^2+4x-3\right)^2-2.\left(x^2+4x-3\right).2,5x+\left(2,5x\right)^2\right]-\left(0,5x\right)^2\)

\(=\left(x^2+4x-3-2,5x\right)^2-\left(0,5x\right)^2\)

\(=\left(x^2+4x-3-2,5x-0,5x\right).\left(x^2-4x-3-2,5x+0,5x\right)\)

\(=\left(x^2+x-3\right).\left(x^2+2x-3\right)\)

Tham khảo nhé~

 Đặt \(x^2-2x=a\) thì \(x^2-2x-1=a-1\)

Ta có: \(\left(x^2-2x\right)\left(x^2-2x-1\right)-6\)

      \(=a\left(a-1\right)-6\)

      \(=a^2-a-6\)

      \(=a^2-3a+2a-6\)

      \(=a\left(a-3\right)+2\left(a-3\right)\)

      \(=\left(a+2\right)\left(a-3\right)\)

      \(=\left(x^2-2x+2\right)\left(x^2-2x-3\right)\)

Cho mình hỏi: Bạn đã biết làm những bài bạn gửi chưa?

2 bài mình mới đăng là mh chỉ để lưu lại, lúc khác làm thôi, dù sao cx cảm ơn bạn