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1.

Simplify the expressions and evaluate them as directed: (i) `x(x-3)+2` for `x=1` (ii) `3y(2y-7)-3(y-4)-63` for `y=2`

Answer» (i) `x(x-3)+2 = x^2-3x+2`
At `x=1, (1)^2-3(1)+2= 1-3+2 = 0`

(ii)`3y(2y-7)-3(y-4)-63 = 6y^2 - 21y -3y+12-63`
`6y^2-24y-51`
At `y=2, 6(2)^2-24(2)-51 = 24-48-51 = -75`
At `y = -2, 6(-2)^2-24(-2)-51 = 24+48-51 = 21`
Discussion
2.

Find the LCM of the following : `(1.) x^3y^2,xyz`.

Answer» `x^3y^2,xyz`
`x^3Xy^2Xz`
`x^3y^2z`.
Discussion
3.

Find the areas of rectangles with the following pairs of monomials as their lengths and breadths respectively(p, q); (10m, 5n); (20x2, 5y2); (4x, 3x2); (3mn, 4np)

Answer» Area=length*breath
1) area = p*q=pq
2) area= 10m*5n=50mn
3) area=`20x^2*5y^2`=`100x^2y^2`
4) area=`4x*3x^2=12x^3`
5) area= 3mn*4np=12mnnp.
Discussion
4.

Use a suitable identity to get each of the following products. (i) `(x+3)(x+3)` (ii) `(2y+5)(2y+5)` (iii) `(2a-7)(2a-7)` (iv) `((3a)-1/2)((3a)-1/2)` (v) `(1.1m-0.4)(1.1m+04)` (vi) `(a^2+b^2)(-a^2+b^2)` (viI) `(6x-7)(6x+7)` (vii) `(-a+c)(-a+c)` (viii) `(x/2+(3y)/4)(x/2+((3y)/4)` (ix) `(7a-9b)(7a-9b)`

Answer» 1)`(x+3)(x+3)=x^2+9+6x`
2)`(2y+5)(2y+5)=4y^2+25+20y`
3)`(2a-7)(2a-7)=4a^2+49-28a`
4)`(3a-1/2)(3a-1/2)=9a^2+1/4-3a`
5)`(1.1m-0.4)(1.1m+0.4)=1.21m^2-0.16`
6)`(b^2+a^2)(b^2-a^2)=b^4-a^4`
7)`(6x-7)(6x+7)=36x^2-49`
8)`(x/2+(3y)/4)^2=x^2/4+(9y^2)/16+(3xy)/4`
9)`(7a-9b)^2=49a^2+81b^2-126ab`.
Discussion
5.

Simplify. (i) `(x^2-5) (x+5)+25` (ii) `(a^2+5) (b^3+3)+5` (iii) `(t+s^2) (t^2-s)` (iv) `(a+b)(c-d)+(9a-b)(c+d)+2(ac+bd)` (v) `(x+y)(2x+y)+(x+2y)+(x+2y)(x-y)` (vi) `(x+y)(x^2-xy+y^2)` (vii) `(1.5x-4y)(1.5x+4y+3)-4.5x+12y` (viii) `(a+b+c)(a+b-c)`

Answer» 1)`(x^2-5)(x+5)+25`
=`x^3+5x^2-5x-25+25`
=`x^3+5x^2-5x`
2)`(a^2+5)(b^3+3)+5`
`a^2b^3+3a^2+5b^3+15+5`
`a^2b^3+3a^2+5b^3+20`
3)`(t+s^2)(t^2-s)`
`t^3-ts+s^2t^2-s^3`4)`(a+b)(c-d)+(9a-b)(c+d)+2(ac+bd)`
`ac+bc-ad-bd+9ac+9ad-bc-bd+2ac+2bd`
`12ac+8ad+2bd-bc`
5)`(x+y)(2x+y)+(x+2y)+(x+2y)(x-y)`
`2x^2+xy+2xy+y^2+x+2y+x^2-xy+2xy-2y^2`
`3x^2+4xy-y^2+x+2y`
6)`(x+y)(x^2-xy+y^2)`
`x^3-x^2y+xy^2+x^2y-xy^2+y^3`
`x^3+y^3`
8)`(a+b+c)(a+b-c)`
`a^2+ab-ac+ab+b^2-bc+ac+bc-c^2`
`a^2+b^2-c^2+2ab`.
Discussion
6.

(a) Subtract `4a-7ab+3b+12` from `12a-9ab+5b` (r) Subtract `3xy+5yz-7zx` from `5xy-2yx+10xyz` (jj) Subtract `4p^2q-3pq+5pq^2-8p+7q-10` from `18-3p-11q+5pq-2pq^2+5p^2q`

Answer» (a) `12a - 9ab + 5b - 3-(4a - 7ab + 3b + 12)`
`= 12a - 4a - 9ab+ 7ab + 5b -3b -3 -12`
`= 8a - 2ab + 2b -15`
(b) `5xy - 2yz-2zx + 10xyz - (3xy + 5yz- 7zx)`
`= 2xy -7yz+5zx + 10zxy`
(c) `18 - 3p - 11q + 5pq - 2pq^2 + 5p^2q-(4p^2q - 3pq + 5pq^2 - 8p+7q-10)`
`= 28 + 5p - 18q + 5pq - 7pq^2 + p^2q + 3pq`
answer
Discussion
7.

Show that. (i) `(3x+7)2-84x=(3x-7)2` (ii) `(9p-5q)2+180pq=(9p+5q)2` (iii) `(43(m)-34(n))2+2mn=169(m2)+916(n2)` (iv) `(4pq+3q)2-(4pq-3q)2=48pq2` (v) `(a-b)(a+b)+(b-c)(b+c)+(c-a)(c+a)=0`

Answer» (i) `L.H.S. = (3x+7)^2 -84x = 9x^2+49+42x - 84x = 9x^2+49-42x`
` = (3x)^2+(7)^2 - 2**3x**7 = (3x-7)^2 = R.H.S.`

(ii)`L.H.S. = (9p-5q)^2+180pq = (9p)^2+(5q)^2-90pq+180pq`
`=(9p)^2+(5q)^2+90pq = (9p)^2+(5q)^2+2(9p)(5q) `
`= (9p+5q)^2 = R.H.S.`

(iii)`L.H.S. = (4/3m-3/4n)^2 +2mn= (4/3m)^2+(3/4n)^2 - 2**(4/3m)**(3/4n)+2mn`
`=16/9m^2+9/16n^2+2mn-2mn = 16/9m^2+9/16n^2 = R.H.S.`

(iv)`L.H.S. = (4pq+3q)^2-(4pq-3q)^2`
Here, we will use `(a+b)(a-b) = a^2-b^2`
So, `L.H.S. = (4pq+3q+4pq-3q)(4pq+3q-4pq+3q)`
` = 8pq**6q = 48pq^2 = R.H.S.`

(v)`L.H.S. = (a-b)(a+b)+(b-c)(b+c)+(c-a)(c+a)`
`= a^2-b^2+b^2-c^2+c^2-a^2 = 0 = R.H.S.`
Discussion
8.

Using Identity find (i) `(4p-3q)^2` (ii) `(49)^2`

Answer» 1) `(4p-3q)^2`
=`16p^2+9q^2-24pq`2)`(49)^2`
`(50-1)^2`
`50^2+1-100`
`2500-100+1`
`2401`.
Discussion
9.

Complete the table for area of a rectangle with given length and breadth.

Answer» Area of rectangle = llength(l) * breadth(b)
(i)Here, length ` = 3x,` breadth` = 5y`
So, Area ` = 3x**5y = 15xy`
(ii)Here, length` = 9y, `breadth `= 4y^2`
So, Area ` = 9y**4y^2 = 36y^3`
(iii)Here, length`= 4ab, `breadth` = 5bc`
So, Area ` = 4ab**5bc= 20ab^2c`
(iv)Here, length` = 2l^2m,` breadth `= 3lm^2`
So, Area ` = 2l^2m**3lm^2= 6l^3m^3`
Discussion
10.

(a) Simpify `3 xx (4x-5)+3` and find its values for (i) `x=3` (ii) `x=1/2.` (j) simplify `a(a^2+a+1)+5` and find its value for (i) `a=0` (ii) `a=1` (iii) `a=-1`

Answer» a)`3x(4x-5)+3=12x^2-15x+3`
when x=3
=12*3*3-15*3+3
=111-45
=66
b)`a(a^2+a+1)+5=a^3+a^2+a+5`
when a=0
=5
when a=1
=1+1+1+5
=8
when a=-1
=-1+1+1+5
=6.
Discussion
11.

Subtract `5x^2 - 4y^2 + 6y - 3` from `7x^2 - 4xy + 8y^2 + 5x - 3y`.

Answer» `7x^2-4xy+8y^2+5x-3y-(5x^2-4y^2+6y-3)`
=`7x^2-4xy+8y^2+5x-3y-5x^2+4y^2-6y+3`
=`2x^2+12y^2-9y-xy+5x-3`.
Discussion
12.

If we subtract `4a - 7ab` from `12a - 9ab` , we get-A. ` 8a + 3ab`B. `8a + 2ab`C. `8a - 2ab`D. none of these

Answer» Correct Answer - C
Discussion
13.

Divide `8a^(3) + 4a^(2)` by `2a`A. `2a(2a + 1)`B. `a(2a + 1)`C. `(2a + 1)`D. none of these

Answer» Correct Answer - A
Discussion
14.

The area of rectange with length `2l^(2)m` and breadth `3lm^(2)` is-A. `l^(3)m^(3)`B. `2l^(3)m^(3)`C. `6l^(3)m^(3)`D. `4l^(3)m^(3)`

Answer» Correct Answer - C
Discussion
15.

Obtain the product of (i) `xy, yz, zx` (ii) `a,-a^2, a^3` (iii) `2, 4y, 8y^2, 16y^3` (iv) `a, 2b, 3c,6abc` (v) `m,-mn, mnp`

Answer» (i) `xyxxyzxxzx = (x xx x)xx(yxxy)xx(zxxz) = x^2y^2z^2`

(ii)`axx(-a^2)xxa^3 = -a^3xxa^3 = -a^6`

(iii)`2xx4yxx8y^2xx16y^3 = 8yxx8y^2xx16y^3`
`=64y^3xx16y^3 = 1024y^6`

(iv)`axx2bxx3cxx6abc = 6abcxx6abc = 36a^2b^2c^2`

(v)`mxx(-mn)xx(mnp) = -m^3xxn^2xxp = -m^3n^2p^2``
Discussion