Question

Completa la Tabla tema productos notables

Answer 1

Respuesta:

$\boxed{\mathbf{\begin{matrix}x&y&x^{2}&2xy&y^{2}&x^{2}+2xy+y^{2}\\\\2a&3b&(2a)^{2}=4a^{2}&2(2a)(3b)=12ab&(3b)^{2}=9b^{2}&4a^{2}+12ab+9b^{2}\\\\6y&9z&(6y)^{2}=36y^{2}&2(6y)(9z)=108yz&(9z)^{2}=81z^{2}&36y^{2}+108yz+81z^{2}\\\\4b&a^{2}&(4b)^{2}=16b^{2}&2(4b)(a^{2})=8a^{2}b&(a^{2})^{2}=a^{4}&16b^{2}+8a^{2}b+a^{4}\\\\\frac{1}{2}r&\sqrt{2}s^{2}&\left(\frac{1}{2}r\right)^{2}=\frac{1}{4}r^{2}&2(\frac{1}{2}r)(\sqrt{2}s^{2})=\sqrt{2}rs^{2}&(\sqrt{2}s^{2})^{2}=2s^{4}&\frac{1}{4}r^{2}+\sqrt{2}rs^{2}+2s^{4}\end{matrix}}}$

Explicación paso a paso:

$\begin{matrix}x&y&x^{2}&2xy&y^{2}&x^{2}+2xy+y^{2}\\\\2a&3b&(2a)^{2}=4a^{2}&2(2a)(3b)=12ab&(3b)^{2}=9b^{2}&4a^{2}+12ab+9b^{2}\\\\6y&9z&(6y)^{2}=36y^{2}&2(6y)(9z)=108yz&(9z)^{2}=81z^{2}&36y^{2}+108yz+81z^{2}\\\\4b&a^{2}&(4b)^{2}=16b^{2}&2(4b)(a^{2})=8a^{2}b&(a^{2})^{2}=a^{4}&16b^{2}+8a^{2}b+a^{4}\\\\\frac{1}{2}r&\sqrt{2}s^{2}&\left(\frac{1}{2}r\right)^{2}=\frac{1}{4}r^{2}&2(\frac{1}{2}r)(\sqrt{2}s^{2})=\sqrt{2}rs^{2}&(\sqrt{2}s^{2})^{2}=2s^{4}&\frac{1}{4}r^{2}+\sqrt{2}rs^{2}+2s^{4}\end{matrix}$