Activity #11 (x + y +5z)²
Answer (1)
AnsweEvaluate the powerEvaluate the powerSolution\(x^{2}+10x+25+y^{2}+25z^{2}+2xy+10y+10xz+50z+10yz\)Step \(\left(x+5+y+5z\right)^{2}\)\(\xpmhighlightbox{bgcolor=#D3E3FD, underlinecolor=#D3E3FD}{\left(x+5+y+5z\right)^{2}}\)Expand the trinomial using formula\(\xpmhighlightbox{bgcolor=#D3E3FD, underlinecolor=#D3E3FD}{\left(x+5\right)^{2}+y^{2}+25z^{2}+2\left(x+5\right)y+2\left(x+5\right)\cdot 5z+10yz}\)Step \(\left(x+5\right)^{2}+y^{2}+25z^{2}+2\left(x+5\right)y+2\left(x+5\right)\cdot 5z+10yz\)\(\xpmhighlightbox{bgcolor=#D3E3FD, underlinecolor=#D3E3FD}{\left(x+5\right)^{2}}+y^{2}+25z^{2}+2\left(x+5\right)y+2\left(x+5\right)\cdot 5z+10yz\)Use \(\left(a+b\right)^{2}=a^{2}+2ab+b^{2}\) to expand the expression\(\xpmhighlightbox{bgcolor=#D3E3FD, underlinecolor=#D3E3FD}{x^{2}+10x+25}+y^{2}+25z^{2}+2\left(x+5\right)y+2\left(x+5\right)\cdot 5z+10yz\)Step \(x^{2}+10x+25+y^{2}+25z^{2}+2\left(x+5\right)y+2\left(x+5\right)\cdot 5z+10yz\)\(x^{2}+10x+25+y^{2}+25z^{2}+\xpmhighlightbox{bgcolor=#D3E3FD, underlinecolor=#D3E3FD}{2\left(x+5\right)y}+2\left(x+5\right)\cdot 5z+10yz\)Distribute \(2y\) through the parentheses\(\xpmhighlightbox{bgcolor=#D3E3FD, underlinecolor=#D3E3FD}{x^{2}+10x+25+y^{2}+25z^{2}+2xy+10y}+2\left(x+5\right)\cdot 5z+10yz\)Step \(x^{2}+10x+25+y^{2}+25z^{2}+2xy+10y+2\left(x+5\right)\cdot 5z+10yz\)\(x^{2}+10x+25+y^{2}+25z^{2}+2xy+10y+\xpmhighlightbox{bgcolor=#D3E3FD, underlinecolor=#D3E3FD}{2\left(x+5\right)\cdot 5z}+10yz\)Calculate the product\(x^{2}+10x+25+y^{2}+25z^{2}+2xy+10y+\xpmhighlightbox{bgcolor=#D3E3FD, underlinecolor=#D3E3FD}{10z}\cdot \left(x+5\right)+10yz\)Step \(x^{2}+10x+25+y^{2}+25z^{2}+2xy+10y+10z\cdot \left(x+5\right)+10yz\)\(x^{2}+10x+25+y^{2}+25z^{2}+2xy+10y+\xpmhighlightbox{bgcolor=#D3E3FD, underlinecolor=#D3E3FD}{10z\cdot \left(x+5\right)}+10yz\)Distribute \(10z\) through the parentheses\(\xpmhighlightbox{bgcolor=#D3E3FD, underlinecolor=#D3E3FD}{x^{2}+10x+25+y^{2}+25z^{2}+2xy+10y+10xz+50z}+10yz\)Solution\(x^{2}+10x+25+y^{2}+25z^{2}+2xy+10y+10xz+50z+10yz\)r:Step-by-step explanation:
