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(i) (x + 2y + 4z)² = x² + (2y)² + (4z)² + 2 × (x) × (2y) + 2 × (2y) × (4z) × (x) [∵ (a + b + c)² = a² + b² + c² + 2ab + 2bc + 2ca] = x² + 4y² + 16x² + 4xy + 16yz + 4zx
y² + √2 Polynomials in one variable as it contains only one variable y.
3√t + t√2 = 3t^1/2 + t√2., It is in one variable but not a polynomial as it contains (t^1/2), in which power is not a whole number.
y + 2/y = y + 2y^-1, It is in one variable but not a polynomial as it contains (y^-1), in which power is not a whole number.
Expand each of the following, using suitable identities: (x + 2y + 4z)²
(i) (x + 2y + 4z)² = x² + (2y)² + (4z)² + 2 × (x) × (2y) + 2 × (2y) × (4z) × (x) [∵ (a + b + c)² = a² + b² + c² + 2ab + 2bc + 2ca] = x² + 4y² + 16x² + 4xy + 16yz + 4zx
(i) (x + 2y + 4z)²
See less= x² + (2y)² + (4z)² + 2 × (x) × (2y) + 2 × (2y) × (4z) × (x) [∵ (a + b + c)² = a² + b² + c² + 2ab + 2bc + 2ca]
= x² + 4y² + 16x² + 4xy + 16yz + 4zx
Which of the following expressions are polynomials in one variable and which are not? State reasons for your answer. y² + √2.
y² + √2 Polynomials in one variable as it contains only one variable y.
y² + √2 Polynomials in one variable as it contains only one variable y.
See lessWhich of the following expressions are polynomials in one variable and which are not? State reasons for your answer. 3√t + t√2.
3√t + t√2 = 3t^1/2 + t√2., It is in one variable but not a polynomial as it contains (t^1/2), in which power is not a whole number.
3√t + t√2 = 3t^1/2 + t√2., It is in one variable but not a polynomial as it contains (t^1/2), in which power is not a whole number.
See lessWhich of the following expressions are polynomial in one variable and which are not? State reasons for your answer. Y + 2/y
y + 2/y = y + 2y^-1, It is in one variable but not a polynomial as it contains (y^-1), in which power is not a whole number.
y + 2/y = y + 2y^-1, It is in one variable but not a polynomial as it contains (y^-1), in which power is not a whole number.
See less