The sum of the polynomials bn - 8am - 8cp, 5cp - am + 2bn and 6am + 5bn - 3cp is equal to

1. -2am + 2bn - 4cp
2. -2am + 8bn - 2cp
3. -3am + 2bn - 4cp
4. -3am + 8bn - 6cp

Fill in the blanks :

(i) The highest power of the …………… in a polynomial is called its degree.

(ii) The degree of the polynomial 7⁵ is …………… .

(iii) Several parts of an algebraic expression separated by + or - signs are called the …………… of the expression.

(iv) Any number is a polynomial of degree …………… .

(v) Terms having the same …………… are called like terms.

(vi) The algebraic expression for the statement ‘the number of times b is contained in x' is …………… .

(vii) 1 + x + y + xy is a polynomial having …………… terms and degree ………….. .

(viii) The length of a side of a square having perimeter 8x² - 2y + 16xy is …………… .

(ix) In a polynomial, the exponents of the variables are always …………… .

(x) If the length of a rectangle having perimeter (6 m² - 2 mn + 2 m²n - 4n²) units, is (3m² + m²n - 2 mn) units, then its breadth is equal to …………… units.

Vasu has a rectangular farmland A. The length of this farmland is x²y - 2xy + 3x² and its perimeter is 2x²y + 6x² - 2xy - 4y². Today he purchased the adjacent farmland B and combined the two farmlands into one. The length of his farmland now increased by x² + xy, while the breadth remained the same.

(1) Find the breadth of farmland A :

1. x²y + 3x² - 4y²
2. xy - 2y²
3. 12x² - 4xy
4. 6x² + xy - 2y²

(2) Find the length of the combined farmland owned by Vasu :

1. x² + 2xy - 2y²
2. 4x² - 3xy + x²y
3. 4x² - xy + x²y
4. 2x² - 3xy + x²y

(3) The perimeter of Vasu's combined farmland is :

1. 8x² + 2x²y - 4y²
2. 4y² + 4xy + 2x²y + 8x²
3. 4x² - 2x²y + 4y²
4. 4x² + 4xy - 2x²y - 8x²

(4) The change in the perimeter after combining farmlands A and B is :

1. 4x² + 2xy + 4x²y - y²
2. 2x² - 2xy + y²
3. 4x² + 2xy - y²
4. 2x² + 2xy