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\(x^4+x^2y^2+y^4=\left(x^4+2x^2y^2+y^4\right)-x^2y^2\)\(=\left(x^2+y^2\right)^2-\left(xy\right)^2=\left(x^2+y^2+xy\right)\left(x^2+y^2-xy\right)\).
Gợi ý:
a) Đặt \(t=x^2+x+1\)
b) Đặt \(t=x^2+8x+11\)
c) \(\left(x+2\right)\left(x+3\right)\left(x+4\right)\left(x+5\right)-24\)
\(=\left[\left(x+2\right)\left(x+5\right)\right].\left[\left(x+3\right)\left(x+4\right)\right]-24\)
\(=\left(x^2+7x+10\right)\left(x^2+7x+12\right)-24\)
Đặt: \(t=x^2+7x+11\)
a) (2x - 1)2 - (x + 3)2
= (2x - 1 - x - 3).(2x - 1 + x + 3)
= (x - 4).(3x + 2)
b) x2.(x - 3) + 12 - 4x
= x2.(x - 3) - 4x + 12
= x2.(x - 3) - 4.(x - 3)
= (x - 3).(x2 - 4)
= (x - 3).(x - 2).(x + 2)
Áp dụng HĐT:
a2 - b2 = (a - b)(a + b)
\(\left(2x-1\right)^2-\left(x+3\right)^2\)
\(=\left(2x-1-x-3\right)\left(2x-1+x+3\right)\)
\(=\left(x-4\right)\left(3x+2\right)\)
a) x2 + 6x + 9 = x2 + 2 . x . 3 + 32 = (x + 3)2
b) 10x – 25 – x2 = -(-10x + 25 +x2) = -(25 – 10x + x2)
= -(52 – 2 . 5 . x – x2) = -(5 – x)2
c) 8x3 - 1/8 = (2x)3 – (1/2)3 = (2x - 1/2)[(2x)2 + 2x . 12 + (1/2)2]
= (2x - 1/2)(4x2 + x + 1/4)
d)1/25x2 – 64y2 = (1/5x)2(1/5x)2- (8y)2 = (1/5x + 8y)(1/5x - 8y)
\(\left(x-1\right)\left(x-2\right)\left(x-3\right)\left(x-4\right)-80=\left(x^2-5x+4\right)\left(x^2-5x+6\right)-80\)
Đặt \(x^2-5x+4=t\), ta có:
\(t\left(t+2\right)-80=t^2-2t+1-81=\left(t-1\right)^2-9^2=\left(t-1-9\right)\left(t-1+9\right)=\left(t-10\right)\left(t+8\right)\)
\(=\left(x^2-5x+4-10\right)\left(x^2-5x+4+8\right)=\left(x^2-5x-6\right)\left(x^2-5x+12\right)\)
\(\left(x^2+x+1\right)\left(x^2+x+2\right)-12\)
Đặt x2 + x + 1 = t, ta có:
t(t + 1) - 12
= t2 + t + 1/4 - 49/4
= (t + 1/2)2 - (7/2)2
= (t + 1/2 + 7/2)(t + 1/2 - 7/2)
= (t + 4)(t - 3)
nhân váo như bình thường sau đó bấm máy tính shift solve =? rồi chia hoocne
a)\(x^4+x^3+x+1=x^3\left(x+1\right)+\left(x+1\right)=\left(x+1\right)\left(x^3+1\right)=\left(x+1\right)^2\left(x^2-x+1\right)\)
b)\(x^4-x^3-x^2+1=\left(x^4-x^3\right)-\left(x^2-1\right)=x^3\left(x-1\right)-\left(x-1\right)\left(x+1\right)\)
\(=\left(x-1\right)\left(x^3-x-1\right)\)
c)\(x^2y+xy^2-x-y=xy\left(x+y\right)-\left(x+y\right)=\left(xy-1\right)\left(x+y\right)\)
x^3-2x-4
=x^3-4x+2x-4
=x(x^2-4)+2(x-2)
=x(x-2)(x+2)+2(x-2)
=(x^2+2x+2)(x-2)
Nhớ cho mình nha!!!
Dễ thôi
\(x^3-x^2-4\)
\(=\left(x^3-8\right)-\left(x^2-4\right)\)
\(=\left(x-2\right)\left(x^2+2x+4\right)-\left(x-2\right)\left(x+2\right)\)
\(=\left(x-2\right)\left(x^2+x+2\right)\)
\(a,\left(x^2+x+1\right)\left(x^2+x+2\right)-12.\)
Đặt \(x^2+x+1=a\)
\(\Rightarrow a\left(a+1\right)-12\)\(=a^2+a-12\)
\(=a^2-3a+4a-12\)
\(=a\left(a-3\right)+4\left(a-3\right)\)
\(=\left(a-3\right)\left(a+4\right)\)
\(=\left(x^2+x+1-3\right)\left(x^2+x+1+4\right)\)
\(=\left(x^2+x-2\right)\left(x^2+x+5\right)\)
\(b,\left(x^2+x\right)^2+4\left(x^2+x\right)-12\)
Đặt \(x^2+x=a\)
\(\Rightarrow a^2+4a-12\)
\(=a^2-2a+6a-12\)
\(=a\left(a-2\right)+6\left(a-2\right)\)
\(=\left(a-2\right)\left(a+6\right)\)
\(=\left(x^2+x-2\right)\left(x^2+x+6\right)\)
\(\left(x^2-x-3\right)\left(x^2-x-4\right)-12\)
\(=x^4-x^3-4x^2-x^3+x^2+4x-3x^2+3x+12-12=x^4-2x^3-6x^2+7x\)
\(=x.\left(x^3-2x^2-6x+7\right)=x.\left(x^3-x^2-x^2+x-7x+7\right)\)
\(=x.\left[x^2.\left(x-1\right)-x.\left(x-1\right)-7.\left(x-1\right)\right]=x\left(x-1\right)\left(x^2-x-7\right)\)