Write the following squares of binomials as trinomials- i-x-22 ii-8a-3b2 iii-2m-12 iv-9a-1-6 2 v-x-x2-2 2 vi-x-4-y-3 2 vii-3x-1-3x 2 viii-x-y-y-x 2 ix-3a-2-5b-4 2 x-a2b-bc22 xi-2a-3b-2b-3a 2 xii-x2-ay2

Using the formulas (a+b)^2=a^2+2ab+b^2 and (a b)^2=a^2 2ab+b^2 (i) (x+2)^2=(x)^2+2× x× 2+(2)^2 { (a+b)^2=a^2+2ab+b^2 } =x^2+4x+4 (ii) (8a+3b)^2=(8a)^2+2× 8a× ...

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Byju's Answer

Standard VIII

Mathematics

Algebraic Identities

Write the fol...

Question

Write the following squares of binomials as trinomials:

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

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

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

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Solution

Using the formulas $(a + b)^{2} = a^{2} + 2 a b + b^{2}$

$a n d (a - b)^{2} = a^{2} - 2 a b + b^{2}$

$(i) (x + 2)^{2} = (x)^{2} + 2 \times x \times 2 + (2)^{2} {(a + b)^{2} = a^{2} + 2 a b + b^{2}} = x^{2} + 4 x + 4 (i i) (8 a + 3 b)^{2} = (8 a)^{2} + 2 \times 8 a \times 3 b + (3 b)^{2} = 64 a^{2} + 48 a b + 9 b^{2} (i i i) (2 m + 1)^{2} = (2 m)^{2} + 2 \times 2 m \times 1 + (1)^{2} = 4 m^{2} + 4 m + 1 (i v) {(9 a + \frac{1}{6})}^{2} = (9 a)^{2} + 2 \times 9 a \times \frac{1}{6} + {(\frac{1}{6})}^{2} = 81 a^{2} + 3 a + \frac{1}{36} (v) {(x + \frac{x^{2}}{2})}^{2} = (x)^{2} + 2 \times x \times \frac{x^{2}}{2} + {(\frac{x^{2}}{2})}^{2} = x^{2} + x^{3} + \frac{x^{4}}{4} (v i) {(\frac{x}{4} - \frac{y}{3})}^{2} = {(\frac{x}{4})}^{2} - 2 \times \frac{x}{4} \times \frac{y}{3} + {(\frac{y}{3})}^{2} = \frac{x^{2}}{16} - \frac{1}{6} x y + \frac{y^{2}}{9} (v i i) {(3 x - \frac{1}{3 x})}^{2} = (3 x)^{2} - 2 \times 3 x \times \frac{1}{3 x} + {(\frac{1}{3 x})}^{2} = 9 x^{2} - 2 + \frac{1}{9 x^{2}} (v i i i) {(\frac{x}{y} - \frac{y}{x})}^{2} = {(\frac{x}{y})}^{2} - 2 \times \frac{x}{y} \times \frac{y}{x} + {(\frac{y}{x})}^{2} = \frac{x^{2}}{y^{2}} - 2 + \frac{y^{2}}{x^{2}} (i x) {(\frac{3 a}{2} - \frac{5 b}{4})}^{2} = {(\frac{3 a}{2})}^{2} - 2 \times \frac{3}{2} a \times \frac{5 b}{4} + {(\frac{5 b}{4})}^{2} = \frac{9 a^{2}}{4} - \frac{15}{4} a b + \frac{25}{16} b^{2} (x) (a^{2} b - b c^{2})^{2} = (a^{2} b)^{2} - 2 a^{2} b \times b c^{2} + (b c^{2})^{2} = a^{4} b^{2} - 2 a^{2} b^{2} c^{2} + b^{2} c^{4} (x i) {(\frac{2 a}{3 b} + \frac{2 b}{3 a})}^{2} = {(\frac{2 a}{3 b})}^{2} + 2 \times \frac{2 a}{3 b} \times \frac{2 b}{3 a} + {(\frac{2 b}{3 a})}^{2} = \frac{4 a^{2}}{9 b^{2}} + \frac{8}{9} + \frac{4 b^{2}}{9 a^{2}} (x i i) (x^{2} - a y)^{2} = (x^{2})^{2} - 2 \times x^{2} \times a y + (a y)^{2} = x^{4} - 2 x^{2} a y + a^{2} y^{2}$

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Similar questions

Q. Write the following squares of binomials as trinomials:
(i) (x + 2)²
(ii) (8a + 3b)²
(iii) (2m + 1)²
(iv)

{(9 a + \frac{1}{6})}^{2}

(v)

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

(vi)

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

(vii)

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

(viii)

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

(ix)

{(\frac{3 a}{2} - \frac{5 b}{4})}^{2}

(x) (a²b − bc²)²
(xi)

{(\frac{2 a}{3 b} + \frac{2 b}{3 a})}^{2}

(xii) (x² − ay)²

If $\frac{2^{(2 a + 1)} \times 3^{(3 b + 2)}}{6^{2}} = 2^{x} \times 3^{y}$

Chose the correct option:

The quadratic curve y = f (x) if it touches the line y = x at the point x = 1 and passes through the point (- 1, 0) is... .

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

Q. Solve the following pair of equations:

\frac{5}{x - 1} + \frac{1}{y - 2} = 2

\frac{6}{x - 1} - \frac{3}{y - 2} = 1

(Where

x \neq 1, y \neq 2)

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Write the following squares of binomials as trinomials: (i) (x+2)2 (ii) (8a+3b)2 (iii) (2m+1)2 (iv) (9a+16)2 (v) (x+x22)2 (vi) (x4−y3)2 (vii) (3x−13x)2 (viii) (xy−yx)2 (ix) (3a2−5b4)2 (x) (a2b−bc2)2 (xi) (2a3b+2b3a)2 (xii) (x2−ay)2