WBBSE Class 7 Mathematics Solutions - কষে দেখি 19.1

সমাধান :

i) $7xy = 7 \times x \times y$

ii) $9x^2y = 3 \times 3 \times x \times x \times y$

iii) $16ab^2c = 2 \times 2 \times 2 \times 2 \times a \times b \times b \times c$

iv) $-25lmn = -5 \times 5 \times l \times m \times n$

v) $12(x+x) = 12(2x) = 24x = 2 \times 2 \times 2 \times 3 \times x$

vi) $-5pq(p^2+8) = -5 \times p \times q \times (p^2+8)$

vii) $21xy^2(3x-2) = 3 \times 7 \times x \times y \times y \times (3x-2)$

viii) $121mn(m^2-n) = 11 \times 11 \times m \times n \times (m^2-n)$

সমাধান :

i) $2xy = 2 \times x \times y$ এবং $33xz = 3 \times 11 \times x \times z$। সাধারণ উৎপাদক: **$x$**।

ii) $14ab = 2 \times 7 \times a \times b$ এবং $21ab = 3 \times 7 \times a \times b$। সাধারণ উৎপাদক: **$7, a, b, 7a, 7b, ab, 7ab$**।

iii) $16mnl = 2 \times 2 \times 2 \times 2 \times m \times n \times l$ এবং $-39nl^2 = -3 \times 13 \times n \times l \times l$। সাধারণ উৎপাদক: **$n, l, nl$**।

iv) $12a^2b = 2 \times 2 \times 3 \times a \times a \times b$, $18ab^2 = 2 \times 3 \times 3 \times a \times b \times b$, $24abc = 2 \times 2 \times 2 \times 3 \times a \times b \times c$। সাধারণ উৎপাদক: **$2, 3, 6, a, b, 2a, 3b, 6ab$**।

v) $2xy = 2 \times x \times y$, $4yz = 2 \times 2 \times y \times z$, $6xz = 2 \times 3 \times x \times z$। সাধারণ উৎপাদক: **$2$**।

vi) $18x^2 = 2 \times 3 \times 3 \times x \times x$, $27x^3 = 3 \times 3 \times 3 \times x \times x \times x$, $-45x = -3 \times 3 \times 5 \times x$। সাধারণ উৎপাদক: **$3, 9, x, 3x, 9x$**।

vii) $5mn = 5 \times m \times n$, $6n^2l^2 = 2 \times 3 \times n \times n \times l \times l$, $7l^2m^2 = 7 \times l \times l \times m \times m$। কোনো সাধারণ উৎপাদক নেই।

সমাধান :

i) **$3x^2, 5x^2$**

ii) **$2x^2y, 4xy^2$**

iii) **$8a^2b, 12a^2c$**

iv) **$6(mn+2), 9(mn+2)$**

v) **$5x(y+2), 10x^2(y+2)$**

সমাধান :

i) $5+10x = 5(1+2x)$

ii) $2x-6 = 2(x-3)$

iii) $7m-14n = 7(m-2n)$

iv) $18xy+21xz = 3x(6y+7z)$

v) $4xy+6yz = 2y(2x+3z)$

vi) $7xyz-6xy = xy(7z-6)$

vii) $7a^2+14a = 7a(a+2)$

viii) $-15m+20 = -5(3m-4)$

ix) $6a^2b+8ab^2 = 2ab(3a+4b)$

x) $3a^2-ab^2 = a(3a-b^2)$

xi) $abc-bcd = bc(a-d)$

xii) $60x^3+4xy-8 = 4(15x^3+xy-2)$

xiii) $x^2y^2z+x^2yz^2 = x^2yz(y+z)$

xiv) $a^3-a^2+a = a(a^2-a+1)$

xv) $x^2y^2z^2+x^2yz^2+x^2y^2q^2 = x^2y^2(z^2+q^2)+x^2yz^2 = x^2y(yz^2+yz^2+yq^2)$ এই প্রশ্নটি অস্পষ্ট।

সমাধান :

i) $xy+2x+y+2 = x(y+2)+1(y+2) = (y+2)(x+1)$

ii) $ab-5b+a-5 = b(a-5)+1(a-5) = (a-5)(b+1)$

iii) $6xy-9y+4x-6 = 3y(2x-3)+2(2x-3) = (2x-3)(3y+2)$

iv) $15m+9-35mn-21n = 3(5m+3)-7n(5m+3) = (5m+3)(3-7n)$

v) $ax+bx-ay-by = x(a+b)-y(a+b) = (a+b)(x-y)$

vi) $c-9+9ab-abc = (c-9)+ab(9-c) = (c-9)-ab(c-9) = (c-9)(1-ab)$