Write the following squares of binomials as trinomials-i x-22ii 8 a-3 b2iii 2 m-12iv 9 a -162v x - x 222vi x4-y3vii 3 x-13 x 2viii xy-yx2ix 3a2-5b42x a2 b-b c22xi 2 a 3 b -2 b 3 a 2- xii x2-a y2

nbsp;We will use the identities a+b2=a2+2ab+b2 #160;and #160;a b2=a2 2ab+b2 to convert the squares of binomials as trinomials. (i) #160;x+22=x2+2 #2 ...

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Byju's Answer

Standard VII

Chemistry

Symbols of Elements and Their Valencies

Write the fol...

Question

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

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Solution

We will use the identities ${(a + b)}^{2} = a^{2} + 2 a b + b^{2} and {(a - b)}^{2} = a^{2} - 2 a b + b^{2}$ to convert the squares of binomials as trinomials.

$(i) {(x + 2)}^{2} = x^{2} + 2 \times x \times 2 + b^{2} = x^{2} + 4 x + b^{2}$

$(ii) {(8 a + 3 b)}^{2} = {(8 a)}^{2} + 2 (8 a) (3 b) + {(6 b)}^{2} = 64 a^{2} + 48 a b + 36 b^{2}$

^{$(iii) {(2 m + 1)}^{2} = {(2 m)}^{2} + 2 (2 m) (1) + 1^{2} = 4 m^{2} + 4 m + 1$

$(iv) {(9 a + \frac{1}{6})}^{2} = {(9 a)}^{2} + 2 (9 a) (\frac{1}{6}) + {(\frac{1}{6})}^{2} = 81 a^{2} + 3 a + \frac{1}{36}$

$(v) {(x + \frac{x^{2}}{2})}^{2} = x^{2} + 2 x (\frac{x^{2}}{2}) + {(\frac{x^{2}}{2})}^{2} = x^{2} + x^{3} + \frac{x^{4}}{4}$

$(vi) {(\frac{x}{4} - \frac{y}{3})}^{2} = {(\frac{x}{4})}^{2} - 2 (\frac{x}{4}) (\frac{y}{3}) + {(\frac{y}{3})}^{2} = \frac{x^{2}}{16} - \frac{1}{6} x y + \frac{y^{2}}{9}$

$(vii) {(3 x - \frac{1}{3 x})}^{2} = {(3 x)}^{2} - 2 (3 x) (\frac{1}{3 x}) + {(\frac{1}{3 x})}^{2} = 9 x^{2} - 2 + \frac{1}{9 x^{2}}$

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

$(ix) {(\frac{3 a}{2} - \frac{5 b}{4})}^{2} = {(\frac{3 a}{2})}^{2} - 2 (\frac{3 a}{2}) (\frac{5 b}{4}) + {(\frac{5 b}{4})}^{2} = \frac{9 a^{2}}{4} - \frac{15 a b}{4} + \frac{25 b^{2}}{16}$

$(x) {(a^{2} b - b c^{2})}^{2} = {(a^{2} b)}^{2} - 2 (a^{2} b) (b c^{2}) + {(b c^{2})}^{2} = a^{4} b^{2} - 2 a^{2} b^{2} c^{2} + b^{2} c^{4}$}

$(xi) {(\frac{2 a}{3 b} + \frac{2 b}{3 a})}^{2} = {(\frac{2 a}{3 b})}^{2} + 2 (\frac{2 a}{3 b}) (\frac{2 b}{3 a}) + {(\frac{2 b}{3 a})}^{2} = \frac{4 a^{2}}{9 b^{2}} + \frac{8}{9} + \frac{4 b^{2}}{9 a^{2}}$

$(xii) {(x^{2} - a y)}^{2} = {(x^{2})}^{2} - 2 x^{2} (a y) + {(a y)}^{2} = x^{4} - 2 x^{2} a y + a^{2} y^{2}$

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Similar questions

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. Classify the following polynomials as monomials, binomials and trinomials:

3 x^{2}, 3 x + 2, x^{2} - 4 x + 2, x^{5} - 7, x^{2} + 3 x y + y^{2}, s^{2} + 3 s t - 2 t^{2}, x y + y z + z x, a^{2} b + b^{2} c, 2 l + 2 m

Q. In the following identify monomials, binomials and trinomials:
(i)

x

(ii)

m^{2} + 2 m

(iii)

3 x y + y + 2 x

(iv)

3 x^{2} + 3 y

(v)

t^{6} - \frac{5}{3} t^{3} + 6

Question 5

Define monomials, binomials, and trinomials. Classify the following into monomials, binomials and trinomials:

$(i) 4 y - 7 x$
$(i i) y^{2}$
$(i i i) x + y - x y$
$(i v) 100$
$(v) a b - a - b$
$(v i) (5 - 3 t)$
$(v i i) 4 p^{2} q - 4 p q^{2}$
$(v i i i) 7 m n$
$(i x) z^{2} - 3 z + 8$
$(x) a^{2} + b^{2}$
$(x i) z^{2} + z$
$(x i i) 1 + x + x^{2}$

Q. Find the squares of the following binomials:

(1) x + 4
(2) 3 + m
(3) 3x + 1
(4) p + 2q
(5) x + 2y

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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+162 (v) x+x222 (vi) x4-y3 (vii) 3x-13x2 (viii) xy-yx2 (ix) 3a2-5b42 (x) (a2b − bc2)2 (xi) 2a3b+2b3a2 (xii) (x2 − ay)2