Find each of the following products- i x-4x-4 ii 2x-3y2x-3y iii 3-4x-5-6y 3-4x-5-6y iv x- 3-x x- 3-x v 1-3x2-9 1-3x2-9 vi 1-2y2-1-3y 1-2y2-1-3y

The correct option is (i) (x 4)(x 4)=(x 4)^2 =(x)^2 2× x × 4+(4)^2 =x^2 8x+16 (ii) (2x 3y)(2x 3y)=(2x 3y)^2 =(2x)^2 2× 2x × 3y +(3y)^2 =4x^2 12xy + 9y^2 ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard VIII

Mathematics

Multiplication of Monomials

Find each of ...

Question

Find each of the following products.
(i) $(x - 4) (x - 4)$
(ii) $(2 x - 3 y) (2 x - 3 y)$
(iii) $(\frac{3}{4} x - \frac{5}{6} y) (\frac{3}{4} x - \frac{5}{6} y)$
(iv) $(x - \frac{3}{x}) (x - \frac{3}{x})$
(v) $(\frac{1}{3} x^{2} - 9) (\frac{1}{3} x^{2} - 9)$
(vi) $(\frac{1}{2} y^{2} - \frac{1}{3} y) (\frac{1}{2} y^{2} - \frac{1}{3} y)$

Open in App

Solution

(i) $(x - 4) (x - 4) = (x - 4)^{2} = (x)^{2} - 2 \times x \times 4 + (4)^{2} = x^{2} - 8 x + 16$

(ii) $(2 x - 3 y) (2 x - 3 y) = (2 x - 3 y)^{2} = (2 x)^{2} - 2 \times 2 x \times 3 y + (3 y)^{2} = 4 x^{2} - 12 x y + 9 y^{2}$

(iii) $(\frac{3}{4} x - \frac{5}{6} y) (\frac{3}{4} x - \frac{5}{6} y) = {(\frac{3}{4} x - \frac{5}{6} y)}^{2} = {(\frac{3}{4} x)}^{2} - 2 \times \frac{3}{4} x \times \frac{5}{6} y + {(\frac{5}{6} y)}^{2} = \frac{9}{16} x^{2} - \frac{5}{4} x y + \frac{25}{36} y^{2}$

(iv) $(x - \frac{3}{x}) (x - \frac{3}{x}) = (x)^{2} - 2 \times x \times \frac{3}{x} + {(\frac{3}{x})}^{2} = x^{2} - 6 + \frac{9}{x^{2}}$

(v) $(\frac{1}{3} x^{2} - 9) (\frac{1}{3} x^{2} - 9) {(\frac{1}{3} x^{2})}^{2} - 2 \times \frac{1}{3} x^{2} \times 9 + (9)^{2} = \frac{1}{9} x^{4} - 6 x^{2} + 81$

(vi) $(\frac{1}{2} y^{2} - \frac{1}{3} y) (\frac{1}{2} y^{2} - \frac{1}{3} y) = {(\frac{1}{2} y^{2} - \frac{1}{3} y)}^{2} = {(\frac{1}{2} y^{2})}^{2} - 2 \times \frac{1}{2} y^{2} \times \frac{1}{3} y + {(\frac{1}{3} y)}^{2} = \frac{1}{4} y^{4} - \frac{1}{3} y^{3} + \frac{1}{9} y^{2}$

Suggest Corrections

Similar questions

Q. Find each of the following products:
(i)

(x - 4) (x - 4)

(ii)

(2 x - 3 y) (2 x - 3 y)

(iii)

(x - \frac{3}{x}) (x - \frac{3}{x})

(iv)

(\frac{1}{3} x^{2} - 9) (\frac{1}{3} x^{2} - 9)

Q. Find each of the following products:
(i) (x − 4)(x − 4)
(ii) (2x − 3y)(2x − 3y)
(iii)

(\frac{3}{4} x - \frac{5}{6} y) (\frac{3}{4} x - \frac{5}{6} y)

(iv)

(x - \frac{3}{x}) (x - \frac{3}{x})

(v)

(\frac{1}{3} x^{2} - 9) (\frac{1}{3} x^{2} - 9)

(vi)

(\frac{1}{2} y^{2} - \frac{1}{3} y) (\frac{1}{2} y^{2} - \frac{1}{3} y)

Q. Factorise.
(1) 2y²−11y+5
(2) x²−2x−80
(3) 3x²−4x+1

Q. Classify the following polynomials based on their degree.
(i)

p (x) = 3

(ii)

p (y) = \frac{5}{2} y^{2} + 1

(iii)

p (x) = 2 x^{3} - x^{2} + 4 x + 1

(iv)

p (x) = 3 x^{2}

(v)

p (x) = x + 3

(vi)

p (x) = - 7

(vii)

p (x) = x^{3} + 1

(viii)

p (x) = 5 x^{2} - 3 x + 2

(ix)

p (x) = 4 x

(x)

p (x) = \frac{3}{2}

(xi)

p (x) = \sqrt{3} x + 1

(xii)

p (y) = y^{3} + 3 y

If $f (x) + 2 f (1 - x) = x^{2} + 1 \forall x ϵ R$ then f(x) is

Join BYJU'S Learning Program

Find each of the following products. (i) (x−4)(x−4) (ii) (2x−3y)(2x−3y) (iii) (34x−56y)(34x−56y) (iv) (x−3x)(x−3x) (v) (13x2−9)(13x2−9) (vi) (12y2−13y)(12y2−13y)