Hãy nhập câu hỏi của bạn vào đây, nếu là tài khoản VIP, bạn sẽ được ưu tiên trả lời.
a. \(9x^2+30x+25=\left(3x+5\right)^2\)
b. \(\dfrac{4}{9}x^4-16x^2=\left(\dfrac{2}{3}x^2-4x\right)\left(\dfrac{2}{3}x^2+4x\right)=x^2\left(\dfrac{2}{3}x-4\right)\left(\dfrac{2}{3}x+4\right)\)
c. \(a^2y^2+b^2x^2-2axby=\left(ay-bx\right)^2\)
d. \(100-\left(3x-y\right)^2=\left(10-3x+y\right)\left(10+3x-y\right)\)
e. \(\dfrac{12}{5}x^2y^2-9x^4-\dfrac{4}{25}y^4=-\left(9x^4-\dfrac{12}{5}x^2y^2+\dfrac{4}{25}y^4\right)=-\left(3x^2-\dfrac{2}{5}y^2\right)^2\)
f. \(64x^2-\left(8a+b\right)^2=\left(8x-8a-b\right)\left(8x+8a+b\right)\)
g. \(27x^3-a^3b^3=\left(3x-ab\right)\left(9x^2+3xab+a^2b^2\right)\)
a) Ta có : 64x2 - (8x + y)2
= (8x)2 - (8x + y)2
= (8x - 8x - y) (8x + 8x + y)
= -y(16x + y)
Bài 1:
a)\(64x^2-(8x+y)^2=-y\left(16x+y\right)\)
b)\((x+y+15)^2-2(x+y+15)+1\)
\(=\left(x+y+14\right)^2\)
c)\(8x^3+60x^2y+150xy^2+125y^3\)
\(=\left(2x+5y\right)^3\)
d)\(x^{16}-1\)
\(=\left(x-1\right)\left(x+1\right)\left(x^2+1\right)\left(x^4+1\right)\left(x^8+1\right)\)
Bài 2:
\(\left(n+7\right)^2-\left(n-5\right)^2\)
\(=\left(n+7+n+5\right)\left(n+7-\left(n+7\right)\right)\)
\(=24\left(n+1\right)\) chia hết 24
1, \(x^2-y^2-2x+2y=\left(x-y\right)\left(x+y\right)-2\left(x-y\right)=\left(x+y-2\right)\left(x-y\right)\)
2, \(x^2-25+y^2+2xy=\left(x+y\right)^2-5^2=\left(x+y-5\right)\left(x+y+5\right)\)
3, \(x^2y-x^3-9y+9x=x^2\left(y-x\right)-9\left(y-x\right)=\left(x-3\right)\left(x+3\right)\left(y-x\right)\)
4, \(x^4+2x^3+x^2=x^2\left(x^2+2x+1\right)=x^2\left(x+1\right)^2\)
5, \(x^4+8x=x\left(x^3+8\right)=x\left(x+8\right)\left(x^2-8x+64\right)\)
a) = (3x)^2 + 2.3x.5+ 5^2 = (3x+5)^2
b) = (2/3x)^2-(4y)^2=(2/3x-4y)(2/3x+4y)
c) = -(9x^4-12/5x^2y^2+4/25y^4) = -[(3x^2)^2 - 2.3x^2.2/5y^2 + (2/5y^2)^2]= -(3x^2-2/5y^2)^2
d) = (x-5)^2 - 4^2= (x-5+4)(x-5-4) = (x-1)(x-9)
e) = (2x)^3 + 3.(2x)^2.(5y) + 3.(2x).(5y)^2 + (5y)^3 = (2x+5y)^3
f) = (8x)^2 - (8a+b)^2 = (8x-8a-b)(8x+8a+b)
g) = (7x-4-2x-1)(7x-4+2x+1) = (5x-5)(9x-3) = 5(x-1).3(x-3)=15(x-1)(x-3)
h) = (x-y)(x+y)- 2(x+y) = (x+y)(x-y-2)
# Chúc bạn học tốt #
Cảm ơn bạn!