Expand- i 8a-3b2 ii 7x-2y2 iii 5x-112 iv a-2-2-a 2 v 3x-4-2y-9 2 vi 9x-102 vii x2y-yz22 viii x-y-y-x 2 ix 3m-4-5n 2

(i) (8a+3b)^2=(8a)^2+2× 8a × 3b + (3b)^2 =64a^2+48ab+9b^2 (ii) (7x+2y)^2=(7x)^2+2× 7x× 2y+(2y)^2 =49x^2+28xy+4y^2 (iii) (5x+11)^2=(5x)^2+2× 5x × 11+(11)^2 =2 ...

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Byju's Answer

Standard VIII

Mathematics

Algebraic Identities

Expand: i 8a+...

Question

Expand:
(i) $(8 a + 3 b)^{2}$
(ii) $(7 x + 2 y)^{2}$
(iii) $(5 x + 11)^{2}$
(iv) ${(\frac{a}{2} + \frac{2}{a})}^{2}$
(v) ${(\frac{3 x}{4} + \frac{2 y}{9})}^{2}$
(vi) $(9 x - 10)^{2}$
(vii) $(x^{2} y - y z^{2})^{2}$
(viii) ${(\frac{x}{y} - \frac{y}{x})}^{2}$
(ix) ${(3 m - \frac{4}{5} n)}^{2}$

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Solution

(i) $(8 a + 3 b)^{2} = (8 a)^{2} + 2 \times 8 a \times 3 b + (3 b)^{2} = 64 a^{2} + 48 a b + 9 b^{2}$

(ii) $(7 x + 2 y)^{2} = (7 x)^{2} + 2 \times 7 x \times 2 y + (2 y)^{2} = 49 x^{2} + 28 x y + 4 y^{2}$

(iii) $(5 x + 11)^{2} = (5 x)^{2} + 2 \times 5 x \times 11 + (11)^{2} = 25 x^{2} + 110 x + 121$

(iv) ${(\frac{a}{2} + \frac{2}{a})}^{2} = {(\frac{a}{2})}^{2} + 2 \times \frac{a}{2} \times \frac{2}{a} + {(\frac{a}{2})}^{2} = \frac{a^{2}}{4} + 2 + \frac{4}{a^{2}}$

(v) ${(\frac{3 x}{4} + \frac{2 y}{9})}^{2} = {(\frac{3}{x})}^{2} + 2 \times \frac{3 x}{4} \times \frac{2 y}{9} + {(\frac{2 y}{9})}^{2} = \frac{9 x^{2}}{16} + \frac{1}{3} x y + \frac{4}{81} y^{2}$

(vi) $(9 x - 10)^{2} = (9 x)^{2} - 2 \times 9 x \times 10 + (10)^{2} = 81 x^{2} - 180 x + 100$

(vii) $(x^{2} y - y z^{2})^{2} = (x^{2} y)^{2} - 2 \times x^{2} y \times y z^{2} + (y z^{2})^{2} = x^{4} y^{2} - 2 x^{2} y^{2} z^{2} + y^{2} z^{4}$

(viii) ${(\frac{x}{y} - \frac{y}{x})}^{2} = {(\frac{x}{y})}^{2} - 2 \times \frac{x}{y} \times \frac{y}{x} + {(\frac{y}{x})}^{2} = \frac{x^{2}}{y^{2}} - 2 + \frac{y^{2}}{x^{2}}$

(ix) ${(3 m - \frac{4}{5} n)}^{2} = (3 m)^{2} - 2 \times 3 m \times \frac{4}{5} n + {(\frac{4}{5} n)}^{2} = 9 m^{2} - \frac{24}{5} m n + \frac{16}{25} n^{2}$

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Similar questions

Q. Expand:
(i) (8a + 3b)²
(ii) (7x + 2y)²
(iii) (5x + 11)²
(iv)

{(\frac{a}{2} + \frac{2}{a})}^{2}

(v)

{(\frac{3 x}{4} + \frac{2 y}{9})}^{2}

(vi) (9x − 10)²
(vii) (x²y − yz²)²
(viii)

{(\frac{x}{y} - \frac{y}{x})}^{2}

(ix)

{(3 m - \frac{4}{5} n)}^{2}

Write the following squares of binomials as trinomials:

$(i) (x + 2)^{2}$ $(i i) (8 a + 3 b)^{2}$ $(i i i) (2 m + 1)^{2}$ $(i v) {(9 a + \frac{1}{6})}^{2}$

$(v) {(x + \frac{x^{2}}{2})}^{2}$ $(v i) {(\frac{x}{4} - \frac{y}{3})}^{2}$ $(v i i) {(3 x - \frac{1}{3 x})}^{2}$ $(v i i i) {(\frac{x}{y} - \frac{y}{x})}^{2}$

$(i x) {(\frac{3 a}{2} - \frac{5 b}{4})}^{2}$ $(x) (a^{2} b - b c^{2})^{2}$ $(x i) {(\frac{2 a}{3 b} + \frac{2 b}{3 a})}^{2}$ $(x i i) (x^{2} - a y)^{2}$

Q. Complete the table of products

$F i r s t m o n o m i a l \to - --------------- \to ↓ S e c o n d m o n o m i a l$	2x	-5y	$3 x^{2}$	-4xy	$7 x^{2} y$	$- 9 x^{2} y^{2}$
2x	$4 x^{2}$	-	-	-	-	-
- 5y	-	-	$- 15 x^{2} y$	-	-	-
$3 x^{2}$	-	-	-	-	-	-
- 4xy	-	-	-	-	-	-
$7 x^{2} y$	-	-	-	-	-	-
$- 9 x^{2} y^{2}$	-	-	-	-	-	-

Q. Find the solution of

7 x + 5 y - 13 z + 4 = 0, 9 x + 2 y + 11 z = 37, 3 x - y + z = 2

and then find

x + y + z

State whether the following statement is true or false.

After Subtracting

- x^{4} + 4 x^{3} y - 8 x^{2} y^{2} + 2 x y^{3} - 4 y^{4}

from

- 5 x^{3} y + x^{2} y^{2} - 6 y^{4}

we get,

x^{4} - 9 x^{3} y + 9 x^{2} y^{2} - 2 x y^{3} - 2 y^{4}

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Expand: (i) (8a+3b)2 (ii) (7x+2y)2 (iii) (5x+11)2 (iv) (a2+2a)2 (v) (3x4+2y9)2 (vi) (9x−10)2 (vii) (x2y−yz2)2 (viii) (xy−yx)2 (ix) (3m−45n)2

Expand:
(i) $(8 a + 3 b)^{2}$
(ii) $(7 x + 2 y)^{2}$
(iii) $(5 x + 11)^{2}$
(iv) ${(\frac{a}{2} + \frac{2}{a})}^{2}$
(v) ${(\frac{3 x}{4} + \frac{2 y}{9})}^{2}$
(vi) $(9 x - 10)^{2}$
(vii) $(x^{2} y - y z^{2})^{2}$
(viii) ${(\frac{x}{y} - \frac{y}{x})}^{2}$
(ix) ${(3 m - \frac{4}{5} n)}^{2}$