10th maths algebra formula
Answers
Answer:
{(a+b)^{2}}\) \(=a^2+2ab+b^{2}\)
\(\mathbf{(a-b)^{2}}\) \(=a^{2}-2ab+b^{2}\)
\(\mathbf{\left (a + b \right ) \left (a – b \right ) }\) \( = a^{2} – b^{2}\)
\(\mathbf{ \left (x + a \right )\left (x + b \right ) }\) \(= x^{2} + \left (a + b \right )x + ab\)
\(\mathbf{\left (x + a \right )\left (x – b \right ) }\) \(= x^{2} + \left (a – b \right )x – ab\)
\(\mathbf{\left (x – a \right )\left (x + b \right )}\) \(= x^{2} + \left (b – a \right )x – ab\)
\(\mathbf{\left (x – a \right )\left (x – b \right ) }\) \(= x^{2} – \left (a + b \right )x + ab\)
\(\mathbf{\left (a + b \right )^{3}}\) \( = a^{3} + b^{3} + 3ab\left (a + b \right )\)
\(\mathbf{\left (a – b \right )^{3} }\) \(= a^{3} – b^{3} – 3ab\left (a – b \right )\)
\(\mathbf{(x + y + z)^{2}}\) \( = x^{2} + y^{2} + z^{2} + 2xy + 2yz + 2xz\)
\(\mathbf{(x + y – z)^{2}}\) \( = x^{2} + y^{2} + z^{2} + 2xy – 2yz – 2xz\)
\(\mathbf{(x – y + z)^{2} }\) \(= x^{2} + y^{2} + z^{2} – 2xy – 2yz + 2xz\)
\(\mathbf{(x – y – z)^{2}}\) \( = x^{2} + y^{2} + z^{2} – 2xy + 2yz – 2xz\)
\(\mathbf{x^{3} + y^{3} + z^{3} – 3xyz }\) \( = (x + y + z)(x^{2} + y^{2} + z^{2} – xy – yz -xz)\)
\(\mathbf{x^{2} + y^{2}}\) \( = \frac{1}{2} \left [(x + y)^{2} + (x – y)^{2} \right ]\)
\(\mathbf{(x + a) (x + b) (x + c) }\) \(= x^{3} + (a + b +c)x^{2} + (ab + bc + ca)x + abc\)
\(\mathbf{x^{3} + y^{3}}\) \(= (x + y) (x^{2} – xy + y^{2})\)
\(\mathbf{x^{3} – y^{3}}\) \( = (x – y) (x^{2} + xy + y^{2})\)
\(\mathbf{x^{2} + y^{2} + z^{2} -xy – yz – zx }\) \( = \frac{1}{2} [(x-y)^{2} + (y-z)^{2} + (z-x)^{2}]\)
Linear Equation in Two Variables
\(\mathbf{a_{1}x + b_{1}y + c_{1} }\)