Hãy nhập câu hỏi của bạn vào đây, nếu là tài khoản VIP, bạn sẽ được ưu tiên trả lời.
\(\left(x+a\right)\left(x+2a\right)\left(x+3a\right)\left(x+4a\right)+a^4.\)
\(=\left(x+a\right)\left(x+4a\right)\left(x+2a\right)\left(x+3a\right)+a^4.\)
\(=\left(x^2+5ax+4a^2\right)\left(x^2+5ax+6a^2\right)+a^4.\)
\(=\left(x+5ax+4a^2+a^2\right)^2.\)
\(=\left(x+5ax+5a^2\right)^2.\)
\(\left(x+a\right)\left(x+2a\right)\left(x+3a\right)\left(x+4a\right)+a^4\)
\(=\)\(\left(x+a\right)\left(x+4a\right)\left(x+2a\right)\left(x+3a\right)+a^4\)
\(=\)\(\left(x^2+5ax+4a^2\right)\left(x^2+5ax+6a^2\right)+a^4\)
\(=\)\(\left[\left(x^2+5ax+5a^2\right)-a^2\right].\left[\left(x^2+5ax+5a^2\right)-a^2\right]+a^4\)
\(=\)\(\left(x^2+5ax+5a^2\right)^2-a^4+a^4\)
\(=\)\(\left(x^2+5ax+5a^2\right)^2\)
Chúc bạn học tốt ~
(x + a)(x + 2a)(x + 3a)(x + 4a) + a4
= (x + a)(x + 4a)(x + 2a)(x + 3a) + a4
= (x2 + 4ax + ax + 4a2)(x2 + 3ax + 2ax + 6a2) + a4
= (x2 + 5ax + 4a2)(x2 + 5ax + 6a2) + a4
Đặt x2 + 5ax + 4a2 = t
= t(t + 2a2) + a4
= (t + a2)2
= (x2 + 5ax + 4a2 + a2)2
= (x2 + 5ax + 5a2)2
\(a.\left(x^2+2x+x+2\right)\left(x^2+5x+6x+30\right)-5\)
\(=\left(x+1\right)\left(x+2\right)\left(x+5\right)\left(x+6\right)-5=\left(x^2+7x+6\right)\left(x^2+7x+10\right)\)
Đặt \(x^2+7x+8=a\Rightarrow\text{Biểu thức }=\left(a-2\right)\left(a+2\right)-5=a^2-9=\left(a-3\right)\left(a+3\right)\)
nên : \(BT=\left(x^2+7x+5\right)\left(x^2+7x+11\right)\)
b.\(BT=\left(x^2+5ax+4a^2\right)\left(x^2+5ax+6a^2\right)+a^4\)
Đặt \(x^2+5ax+5a^2=y\Rightarrow BT=\left(y-a^2\right)\left(y+a^2\right)+a^4=y^2=\left(x^2+5ax+5a^2\right)^2\)