Question

Выполните разложение многочленов на множители
A) 20y²-20a²
Б) 32x²+64xy+32y²
B) 12c³-12y³
Г) 45а⁴-45х4​

Answer 1

$\displaystyle\bf\\1)\\\\20y^{2} -20a^{2} =20\cdot(y^{2} - a^{2} )=20(y-a)(y+a)\\\\2)\\\\32x^{2} +64xy+32y^{2} =32\cdot(x^{2} +2xy+y^{2} )=32(x+y)^{2} \\\\3)\\\\12c^{3} -12y^{3} =12\cdot(c^{3} -y^{3} )=12(c-y)(c^{2} +cy+y^{2} )\\\\4)\\\\45a^{4} -45x^{4} =45\cdot(a^{4} -x^{4} )=45(a^{2} +x^{2} )(a^{2} -x^{2} )=\\\\=45(a^{2}+ x^{2} )(a+x)(a-x)$

Answer 2

Ответ:

$20y^2-20a^2= 20(y^2-a^2)=20(y-a)(y+a)$

$32x^2+64xy+32y^2=32(x^2+2xy+y^2)=32(x+y)^2$

$12c^3-12y^3 = 12(c^3-y^3) = 12(c-y)(c^2+cy+y^2)$

$45a^4-45*4=45(a^4-4) = 45 ((a^2)^2-4) = 45 (a^2-2)(a^2+2)$