b) \(25-x^2+14xy-49y^2\)

\(=25-\left(x^2-14xy+49y^2\right)\)

\(=25-\left[x^2-2\cdot7y\cdot x+\left(7y\right)^2\right]\)

\(=25-\left(x-7y\right)^2\)

\(=5^2-\left(x-7y\right)^2\)

\(=\left[5-\left(x-7y\right)\right]\left[5+\left(x-7y\right)\right]\)

\(=\left(5-x+7y\right)\left(5+x-7y\right)\)

c) \(x^5+x^4+1\)

\(=x^5+x^4+1+x^3-x^3\)

\(=\left(x^5+x^4+x^3\right)+\left(1-x^3\right)\)

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

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

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

b: 25-x^2+14xy-49y^2

=25-(x-7y)^2

=(5-x+7y)(5+x-7y)

c: =x^5+x^4+x^3+1-x^3

=x^3(x^2+x+1)+(1-x)(x^2+x+1)

=(x^2+x+1)(x^3+1-x)

\(14x^2-14xy-8x+8y=14x\left(x-y\right)-8\left(x-y\right)=\left(x-y\right)\left(14x-8\right)\)

\(14x^2-14xy-8x+8y\)

\(=14x\left(x-y\right)-8\left(x-y\right)\)

\(=\left(14x-8\right)\left(x-y\right)\)

\(=2\left(7x-4\right)\left(x-y\right)\)

\(14x^2-14xy-8y+8y=2\left(x-y\right)\left(7x-4\right)\)

ta có :\(5x^2-10xy+5y^2-20z^2=5\left(x^2-2xy+y^2-4z^2\right)=5\left(\left(x-y\right)^2-\left(2z\right)^2\right)=5\left(x-y-2z\right)\left(x-y+2z\right)\)

= ( 7x² + 14xy + y² ) - 1

= ( 7x + y )² - 1

= [(7x + y) + 1] [( 7x + y) - 1]

49.x^2 - 1 + 14xy + y^2
= (49.x^2 + 14xy + y^2) - 1
= (7x + y)^2 - 1
= (7x + y + 1)(7x + y - 1)

Áp dụng hằng đẳng thức hiệu 2 bình phương .

\(4x^2-3y^2\)

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

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

_ Chúc bạn học tốt _

a: \(x^2+4xy+y^2\)

\(=x^2+4xy+4y^2-3y^2\)

\(=\left(x+2y-y\sqrt{3}\right)\left(x+2y+y\sqrt{3}\right)\)

Đề sai nhé .Sửu lại

\(x^2-4x^2y^2+4+4x\)

\(=\left(x^2+4x+4\right)-4x^2y^2\)

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

\(=\left(x+2+2xy\right)\left(x+2-2xy\right)\)

\(\dfrac{xy}{2}-x+\dfrac{x^2}{4}=x\left(\dfrac{y}{2}-1+\dfrac{x}{4}\right)\)