1) Phân tích các đa thức sau thành nhân tử
a) ( x-y+4)^2 - ( 2x+3y-1)^2
b) 9x^2 + 90x + 225 - (x-7)^2
c) 49(y-4)^2 - 9y^2 - 36y - 36
d) x^2 - 5x - 14
2) Tính nhanh
a) 202^2 - 54^2 + 256. 352
b) 621^2 - 769. 373 - 148^2
3) Tìm GTNN của biểu thức
A = 5x^2 + 2y^2 + 2xy - 4x - 2y + 11
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a, \(\left(x-y+4\right)^2-\left(2x+3y-1\right)^2=\left(x-y+4+2x+3y-1\right)\left(x-y+4-2x-3y+1\right)\)
\(=\left(3x+2y+3\right)\left(-x-4y+5\right)\)
b, \(x^6+y^6=\left(x^2\right)^3+\left(y^2\right)^3=\left(x^2+y^2\right)\left(x^4-x^2y^2+y^4\right)\)
c, \(x^{16}-1=\left(x^2\right)^8-1=\left[\left(x^2\right)^4\right]^2-1=\left(x^8-1\right)\left(x^8+1\right)\)
\(\left(x-y+4\right)^2-\left(2x+3y-1\right)^2\)
\(=\left(x-y+4+2x+3y-1\right)\left(x-y+4-2x-3y+1\right)\)
\(=\left(3x+2y+3\right)\left(-x-4y+5\right)\)
\(49\left(y-4\right)^2-9y^2-36y-36\)
\(=49\left(y-4\right)^2-\left(9y^2+36y+36\right)\)
\(=49\left(y-4\right)^2-\left(3y+6\right)^2\)
\(=[7\left(y-4\right)]^2-\left(3y+6\right)^2\)
\(=\left(7y-28\right)^2-\left(3y+6\right)^2\)
\(=\left(7y-28+3y+6\right)\left(7y-28-3y-6\right)\)
\(=\left(10y-22\right)\left(4y-34\right)\)
B1:
a) \(9x^2+90x+225-\left(x-7\right)^2\)
= \(9x^2+90x+225-x^2+14x-49\)
= \(8x^2+104x+176\)
= \(\left(x+2\right)\left(x+11\right)\)
b) \(49\left(y-4\right)^2-9y^2-36y+36\)
= \(49\left(y^2-8y+16\right)-9y^2-36y+36\)
= \(49y^2-392y+784-9y^2-36y+36\)
= \(40y^2-428y+820\)
= \(\left(5y-41\right)\left(8y-20\right)\)
B2:
a) A = \(xy-4y-5y+20=xy-9y+20\)
A = \(y\left(x-9\right)+20\)
Với x = 14, y = \(\dfrac{11}{2}\)
A = \(\dfrac{11}{2}\left(14-9\right)+20=47,5\)
b) B = \(x^2+xy-5x-5y\)
B = \(x\left(x+y\right)-5\left(x+y\right)=\left(x+y\right)\left(x-5\right)\)
Với x = -5, y = -8
B = \(\left(-5-8\right)\left(-5-5\right)=130\)
B3:
a) \(4x^2-25-\left(2x-5\right)\left(2x+7\right)=0\)
\(\left(2x-5\right)\left(2x+5\right)-\left(2x-5\right)\left(2x+7\right)=0\)
\(\left(2x-5\right)\left(2x+5-2x-7\right)=0\)
\(\left(2x-5\right)\left(-2\right)=0\)
\(x=\dfrac{5}{2}\)
b) \(\left(x^3+27\right)+\left(x+3\right)\left(x-9\right)=0\)
\(\left(x+3\right)\left(x^2-3x+9\right)+\left(x+3\right)\left(x-9\right)=0\)
\(\left(x+3\right)\left(x^2-3x+9+x-9\right)=0\)
\(\left(x+3\right)x\left(x-2\right)=0\)
\(\left[{}\begin{matrix}x=-3\\x=0\\x=2\end{matrix}\right.\)
c) \(\left(2x^3+2x^2\right)+\left(3x^2+3\right)=0\)
\(2x^3+5x^2+3=0\)
\(\Rightarrow\) Đề sai rồi, nghiệm khủng bố lắm.
Câu 2 nha
\(a,x^4+2x^3+x^2\)
\(=x^2\left(x^2+2x+1\right)\)
\(=x^2\left(x+1\right)^2\)
\(c,x^2-x+3x^2y+3xy^2+y^3-y\)
\(=\left(x^3+3x^2y+3xy^2+y^3\right)-\left(x+y\right)\)
\(=\left(x+y\right)^3-\left(x+y\right)\)
\(=\left(x+y\right)\left(x^2+2xy+y^2-1\right)\)
\(b,9x^2+90x+225-\left(x-y\right)^2\)
\(=\left(3x+15\right)^2-\left(x-y\right)^2\)
\(=\left(3x+15-x+y\right)\left(3x+15+x-y\right)\)
\(=\left(2x+y+15\right)\left(4x-y+15\right)\)
Bài 1 :
x2-2x+2>0 với mọi x
=x2-2.x.1/4+1/16+31/16
=(x-1/4)2 + 31/16
Vì (x-1/4)2 \(\ge\) 0 nên (x-1/4)2 + 31/16 \(\ge\) 0 với mọi x (đfcm)
a/Dùng hằng đẳng thức A2-B2=(A+B)(A-B) phân tích được ngay
\(\left(x-y+4\right)^2-\left(2x+3y-1\right)^2\)
\(=\left(x-y+4+2x+3y-1\right)\left(x-y+4-2x-3y+1\right)\)
=\(\left(3x-2y+3\right)\left(4-x-4y\right)\)
b/Chắc chỉ phân tích hằng đẳng thức (A-B)2=A2-2ab+B2
\(49\left(y-4\right)^2-9y^2-3y-36=49y^2-392y+784-9y^2-3y-36\)
\(=40y^2-395y+748\)
Mình dùng biệt thức cho ra nghiệm vô tỉ, không biết cho phải tại mình tính sai hay đề thiếu nữa
c/Khai triển biểu thức ban đầu ta được
\(x\left(x-y\right)+y\left(y-x\right)=x^2-xy+y^2-xy=x^2-2xy+y^2=\left(x-y\right)^2\)
2)Tính nhanh:
a)\(202^2-54^2+256.352\)
\(=\left(202-54\right)\left(202+54\right)+256.352\)
\(=148.256+256.352\)
\(=256\left(148+352\right)\)
\(=256.500\)
\(=128000\)
b)\(621^2-769.373-148^2\)
\(=621^2-148^2-769.373\)
\(=\left(621-148\right)\left(621+148\right)-769.373\)
\(=473.769-769.373\)
\(=769\left(473-373\right)\)
\(=769.100\)
\(=76900\)
\(a,\left(x-y+4\right)^2-\left(2x+3y-1\right)^2\)
\(=\left(x-y+4-2x-3y+1\right)\left(x-y+4+2x+3y-1\right)\)
\(=\left(-x-4y+5\right)\left(3x+2y+3\right)\)
\(b,9x^2+90x+225-\left(x-7\right)^2\)
\(=9\left(x^2+10x+25\right)-\left(x-7\right)^2\)
\(=9\left(x+5\right)^2-\left(x-7\right)^2\)
\(=\left[3\left(x+5\right)\right]^2-\left(x-7\right)^2\)
\(=\left(3x+15\right)^2-\left(x-7\right)^2\)
\(=\left(3x+15-x+7\right)\left(3x+15+x-7\right)\)
\(=\left(2x+22\right)\left(4x+8\right)\)
\(=2\left(x+11\right).4\left(x+2\right)\)
\(=8\left(x+2\right)\left(x+11\right)\)
\(c,49\left(y-4\right)^2-9y^2-36y-36\)
\(=\left\{\left[7\left(y-4\right)\right]^2-\left(3y\right)^2\right\}-\left(36y+36\right)\)
\(=\left(7y-28-3y\right)\left(7y-28+3y\right)-36\left(y+1\right)\)
\(=\left(4y-28\right)\left(10y-28\right)-36\left(y+1\right)\)
\(=4\left(y-7\right)2\left(5y-14\right)-36\left(y+1\right)\)
\(=8\left(y-7\right)\left(5y-14\right)-36\left(y+1\right)\)
\(=4\left[2\left(y-7\right)\left(5y-14\right)-9\left(y+1\right)\right]\)
mk ko chắc là câu này mk lm đg
\(d,x^2-5x-14\)
\(=x^2+2x-7x-14\)
\(=x\left(x+2\right)-\left(7x+14\right)\)
\(=x\left(x+2\right)-7\left(x+2\right)\)
\(=\left(x+2\right)\left(x-7\right)\)