1)4y^2-(y-c)^2= 2)(a^2+2ab+b^2)-c^2= 3)1-a^2-2ab-b^2= 4)a^2-b^2+a+b= 5)x-y-x^2+y^2= ...

Question

1)4y^2-(y-c)^2=
2)(a^2+2ab+b^2)-c^2=
3)1-a^2-2ab-b^2=
4)a^2-b^2+a+b=
5)x-y-x^2+y^2=
6)m^5-m^3+m^2-1=
(Можно с решением)

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Comments

разложить на множители?

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Да

Answer 1

1)4y²-(y-c)²=(2y-y+c)(2y+y-c)=(y+c)(3y-c)
2)(a²+2ab+b²)-c²=(a+b)²-c²=(a+b-c)(a+b+c)
3)1-a²-2ab-b²=1-(a²+2ab+b²)=1-(a+b)²=(1-a-b)(1+a+b)
4)a²-b²+a+b=(a-b)(a=b)+(a+b)=(a+b)(a-b+1)
5)x-y-x²+y²=(x-y)-(x²-y²)=(x-y)-(x-y)(x+y)=(x-y)(1-x-y)
6)m^5-m^3+m²-1=m³(m²-1)+(m²-1)=(m²-1)(m³+1)=
=(m-1)(m+1)(m+1)(m²-m+1)=(m+1)²(m-1)(m²-m+1)

Answer 2

4у^2 - ( у - с )^2 = ( 2у )^2 - ( у - с )^2 = ( 2у + у - с )( 2у - у + с ) = ( у - с )( у + с )
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( а^2 + 2аb + b^2 ) - c^2 = ( a + b )^2 - c^2 = ( a + b + c )( a + b - c )
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1 - a^2 - 2ab - b^2 = 1 - ( a - b )^2 = ( 1 + a - b )( 1 - a + b )
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a^2 - b^2 + a + b = ( a - b )( a + b ) + ( a + b ) = ( a + b )( a - b + 1 )
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x - y - x^2 + y^2 = ( x - y ) - ( x^2 - y^2 ) = ( x - y ) - ( x - y )( x + y ) = ( x - y )( 1 - ( x + y )) = ( x - y )( 1 - x - y )
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m^5 - m^3 + m^2 - 1 = m^3( m^2 - 1 ) + ( m^2 - 1 ) = ( m^2 - 1 )( m^3 + 1 ) = ( m - 1 )( m + 1 )( m + 1 )( m^2 - m + 1 ) = ( m - 1 )•( m + 1 )^2•( m^2 - m + 1 )