Answer:
Given: \((x+y)(x-y) + (y+z)(y-2) + (z + x)(z − x) + 7\)
Step 1: Expand each expression separately.
\((x+y)(x-y) = x^2 - xy + xy - y^2 = x^2 - y^2\)
\((y+z)(y-2) = y^2 - 2y + yz - 2z\)
\((z + x)(z − x) = z^2 - x^2\)
Step 2: Combine the expanded expressions:
\(x^2 - y^2 + y^2 - 2y + yz - 2z + z^2 - x^2 + 7\)
Step 3: Simplify the equation:
\(x^2 - x^2 - y^2 + y^2 + z^2 - 2y + yz - 2z + 7\)
Step 4: Combine like terms:
\(-2y + yz - 2z + 7\)
This is the simplified form of the expression \((x+y)(x-y) + (y+z)(y-2) + (z + x)(z − x) + 7\).
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Answers & Comments
Verified answer
Given :
[tex] = (x + y)(x - y) + (y + z) \\ (y - 2) + (z + x)(z - x) \\ + 7[/tex]
Solution Explanation :
[tex] = (x + y)(x - y) + (y + z) \\ (y - 2) + (z + x)(z - x) \\ + 7 \\ \\ = {x}^{2} - {y}^{2} + y(y - 2) \\ + z(y - 2) + {z}^{2} - {x}^{2} + 7 \\ \\ = {x}^{2} - {y}^{2} + {y}^{2} - 2y + zy \\ - 2z + {z}^{2} - {x}^{2} + 7 \\ \\ = {\cancel{ {x}^{2} }} - {\cancel{ {x}^{2} }} - {\cancel{ {y}^{2} }} + {\cancel{ {y}^{2} }} - 2y \\ - 2z + {z}^{2} + 7 \\ \\ = - 2y - 2z + {z}^{2} + 7[/tex]
Answer:
Given: \((x+y)(x-y) + (y+z)(y-2) + (z + x)(z − x) + 7\)
Step 1: Expand each expression separately.
\((x+y)(x-y) = x^2 - xy + xy - y^2 = x^2 - y^2\)
\((y+z)(y-2) = y^2 - 2y + yz - 2z\)
\((z + x)(z − x) = z^2 - x^2\)
Step 2: Combine the expanded expressions:
\(x^2 - y^2 + y^2 - 2y + yz - 2z + z^2 - x^2 + 7\)
Step 3: Simplify the equation:
\(x^2 - x^2 - y^2 + y^2 + z^2 - 2y + yz - 2z + 7\)
Step 4: Combine like terms:
\(-2y + yz - 2z + 7\)
This is the simplified form of the expression \((x+y)(x-y) + (y+z)(y-2) + (z + x)(z − x) + 7\).