Question

Правильно ли это? 1.а) (у - 4)^2=у^2-8у+16 б) (7х + а)^2=48х^2+14ах+а^2 в) (5с - 1) (5с + 1)=25с^2-1 г) (3а + 2b) (3а - 2b)=9в^2-4b^2 2.(а - 9)^2 - (81 + 2а)=a^2-18a+81-81-2a= =a^2-20a 3.а) х^2 - 49=(x-7)(x+7) б) 25х^2 - 10ху + у^2=(5x-y)(5x-y) 4.(2 - х)^2 - х (х + 1,5) = 4. 4-4x+x^2-x^2-1,5x=4 -6,5x=4-4 x=0 5.а) (у^2 - 2а) (2а + у^2)=-4a^2+y^4 б) (3х^2 + х)^2=9x^4+6x^3+x^2 в) (2 + m)^2 (2 - m)^2= =(4+4m+m^2)(4-4m+m^2)= =m^4-8m+16 6. а) 4х^2y^2 - 9а^4=(2xy-3a)(2xy+3a) б) 25а^2 - (а + 3)^2=24a^2-6a-9= =3(2a+1)(4a-3) в) 27m^3 + n^3=(3m+n)(9m^2-3mn+n^2)

Answer 1

Г) (3а + 2b) (3а - 2b)=9а^2-4b^2
б) (7х + а)^2=49х^2+14ах+а^2

2.(а - 9)^2 - (81 + 2а)=a^2-18a+81-81-2a=

=a^2-20a
в) (2 + m)^2 (2 - m)^2=

=(4+4m+m^2)(4-4m+m^2)=

=m^4-8m^2+16
б) 25х^2 - 10ху + у^2=(5x-y)(5x-y)

4.(2 - х)^2 - х (х + 1,5) = 4.

4-4x+x^2-x^2-1,5x=4

-5,5x=4-4

x=0
а) 4х^2y^2 - 9а^4=(2xy-3a^2)(2xy+3a^2)

Answer 2

Let's go through each expression one by one to check their correctness:

a) $(u - 4)^2 = u^2 - 8u + 16$ - Correct b) $(7x + a)^2 = 48x^2 + 14ax + a^2$ - Correct c) $(5c - 1)(5c + 1) = 25c^2 - 1$ - Correct d) $(3a + 2b)(3a - 2b) = 9a^2 - 4b^2$ - Correct

$(a - 9)^2 - (81 + 2a) = a^2 - 18a + 81 - 81 - 2a = a^2 - 20a$ - Correct

a) $x^2 - 49 = (x - 7)(x + 7)$ - Correct b) $25x^2 - 10xy + y^2 = (5x - y)(5x - y)$ - Incorrect. The correct factorization is $25x^2 - 10xy + y^2 = (5x - y)^2$

$(2 - x)^2 - x(x + 1.5) = 4 - 4x + x^2 - x^2 - 1.5x = 4 - 6.5x$ - Incorrect. The correct simplification is $(2 - x)^2 - x(x + 1.5) = 4 - 4x + x^2 - x^2 - 1.5x = 4 - 5.5x$

a) $(y^2 - 2a)(2a + y^2) = -4a^2 + y^4$ - Correct b) $(3x^2 + x)^2 = 9x^4 + 6x^3 + x^2$ - Correct c) $(2 + m)^2(2 - m)^2 = (4 + 4m + m^2)(4 - 4m + m^2) = m^4 - 8m^2 + 16$ - Incorrect. The correct expansion is $(2 + m)^2(2 - m)^2 = (4 + 4m + m^2)(4 - 4m + m^2) = m^4 - 16$.

a) $4x^2y^2 - 9a^4 = (2xy - 3a)(2xy + 3a)$ - Correct b) $25a^2 - (a + 3)^2 = 24a^2 - 6a - 9 = 3(8a - 3)(a + 1)$ - Correct c) $27m^3 + n^3 = (3m + n)(9m^2 - 3mn + n^2)$