Question 11 Mark
Simplify:$(x+y)\left(x^2-x y+y^2\right)$
AnswerWe have $(x+y)\left(x^2-x y+y^2\right)$
$(x+y)\left(x^2-x y+y^2\right)=x\left(x^2-x y+y^2\right)+y\left(x^2-x y+y^2\right)$
$=x^3-x^2 y+x y^2+x^2 y-x y^2+y^3$
$=x^3+y^3$
View full question & answer→Question 21 Mark
Simplify: $\left(t+s^2\right)\left(t^2-s\right)$
Answer$\left(t+s^2\right)\left(t^2-s\right)=t\left(t^2-s\right)+s^2\left(t^2-s\right)$
$=t \times t^2-t \times s+s^2 \times t^2-s^2 \times s$
$=t^3-s t+s^2 t^2-s^3$
View full question & answer→Question 31 Mark
Find the product: $\left(p^{2}-q^{2}\right)(2 p+q)$
Answer$\left(p^{2}-q^{2}\right)(2 p+q)$
$=p^{2} (2 p+q)-q^{2}(2 p+q)$
$=p^{2} \times 2 p+p^{2} \times q-q^{2} \times 2 p-q^{2} \times q$
$=2 p^{3}+p^{2} q-2 p q^{2}-q^{3}$
View full question & answer→Question 41 Mark
Find the product of $\left(a^2+b\right)$ and $\left(a+b^2\right)$
AnswerProduct of $\left(a^2+b\right)$ and $\left(a+b^2\right)$
$\left(a^2+b\right)\left(a+b^2\right)=a^2\left(a+b^2\right)+b\left(a+b^2\right) $
$=a^3+a^2 b^2+a b+b^3$
View full question & answer→Question 51 Mark
Find the product: $(x + 7y)(7x - y)$
Answer$(x + 7y)(7x - y)$
$= x(7x - y) + 7y (7x - y)$
$= x \times 7x - x \times y + 7y \times 7x - 7y \times y$
$= 7x^2- xy + 49xy - 7y^2$
$= 7x^2+ 48xy - 7y^2$
View full question & answer→Question 61 Mark
Find the product: $(5 - 2x)(3 + x)$
Answer$(5 - 2x)(3 + x)$
$= 5(3 + x) - 2x(3 + x)$
$= 5 \times 3 + 5 \times x - 2x \times 3 - 2x \times x$
$= 15 + 5x - 6x - 2x^2= 15 - x - 2x^2$
View full question & answer→Question 71 Mark
Multiply the binomials $(a + 3b)$ and $(x + 5)$
AnswerProduct of $(a + 3b)$ and $(x + 5)$
$(a + 3b)(x + 5) = a(x + 5) + 3b (x + 5)$
$= ax + 5a + 3bx + 15b = ax + 3bx + 5a+ 15b$
View full question & answer→Question 81 Mark
Multiply the binomials: $(y - 8)$ and $(3y - 4)$
Answer$(y - 8) \times (3y - 4) = y(3y - 4) - 8(3y - 4)$
$= y \times 3y - y \times 4 - 8 \times 3 y - 8 \times -4$
$= 3y^2- 4y - 24y + 32$
$= 3y^2- 28y + 32$
View full question & answer→Question 91 Mark
Subtract: $3l(l - 4m + 5n)$ from $4l(10n - 3m + 2l)$
Answer$4l(10n - 3m + 2l) - 3l(l - 4m + 5n)$
$= 40ln - 12lm + 8l^2- 3l^2+ 12lm - 15ln$
$= 8l^2- 3l^2- 12lm + 12lm + 40ln - 15ln$
$= 5l^2+ 25ln$
View full question & answer→Question 101 Mark
Add: $p(p - q), q(q - r)$ and $r(r - p).$
Answer$p(p - q) + q(q - r) + r(r - p)$
$=p^{2}-p q+q^{2}-q r+r^{2}-r p$
$=p^{2}+q^{2}+r^{2}-p q-q r-r p$
View full question & answer→Question 111 Mark
Simplify $a (a^2+ a + 1) + 5$ and find its value for $a = 0$
AnswerWe have $a(a^2+ a + 1) + 5 = a^3+ a^2+ a + 5$
Now substituting $a = 0$ in the expression
$a^3+ a^2+ a + 5 = 0^3+ 0^2+ 0 + 5$
$= 0 + 0 + 0 + 5 = 5$
View full question & answer→Question 121 Mark
Find the product: $x \times x^{2} \times x^{3} \times x^{4}$
Answer$x \times x^{2} \times x^{3} \times x^{4}=x^{1+2+3+4}=x^{10}$
View full question & answer→Question 131 Mark
Find the product: $\left(\frac{-10}{3} p q^{3}\right) \times\left(\frac{6}{5} p^{3} q\right)$
Answer$\left(\frac{-10}{3} p q^{3}\right) \times\left(\frac{6}{5} p^{3} q\right)$$=\left(\frac{-10}{3} \times \frac{6}{5}\right)\left(p \times p^{3} \times q^{3} \times q\right)$
$= -4p^4q^4$
View full question & answer→Question 141 Mark
Find the product: $\left(\frac{2}{3} x y\right) \times\left(\frac{-9}{10} x^{2} y^{2}\right)$
Answer$\left(\frac{2}{3} x y\right) \times\left(\frac{-9}{10} x^{2} y^{2}\right)$$=\left(\frac{2}{3} \times \frac{-9}{10}\right)\left(x \times x^{2} \times y \times y^{2}\right)$
$=\frac{-3}{5} x^{3} y^{3}$
View full question & answer→Question 151 Mark
Find the product: $\left(a^{2}\right) \times\left(2 a^{22}\right) \times\left(4 a^{26}\right)$
Answer$\left(a^{2}\right) \times\left(2 a^{22}\right) \times\left(4 a^{26}\right)$ $=(2 \times 4)\left(a^{2} \times a^{22} \times a^{26}\right)$
= $8 \times a^{2+22+26}=8 a^{50}$
View full question & answer→Question 161 Mark
Find the multiplication of the expressions: $pq + qr + rp, 0$
Answer$(p q+q r+r p) \times 0=p q \times 0+q r \times 0+r p \times 0 = 0 + 0 + 0 = 0$
View full question & answer→Question 171 Mark
Find the multiplication of the expressions: $a^2- 9, 4a$
Answer$\left(a^{2}-9\right) \times 4 a=a^{2} \times 4 a-4 a \times 9=4 a^{3}-36 a$
View full question & answer→Question 181 Mark
Find out the multiplication of the expressions:$ a + b, 7a^2b^2$
Answer$(a+b) \times 7 a^{2} b^{2}=a \times 7 a^{2} b^{2}+b \times 7 a^{2} b^{2}=7 a^{3} b^{2}+7 a^{2} b^{3}$
View full question & answer→Question 191 Mark
Find the multiplication of the expressions: $ab, a - b$
Answer$a b \times(a-b)=a b \times a-a b \times b= a^{2} b-a b^{2}$
View full question & answer→Question 201 Mark
Find the multiplication of the expressions: $4p, q + r$
Answer$4 p \times(q+r)=4 p \times q+4 p \times r = 4pq + 4pr$
View full question & answer→Question 211 Mark
Obtain the product of $m, -mn, mnp.$
Answer$m\times (-mn)\times mnp$
$= -m^3n^2p$
View full question & answer→Question 221 Mark
Obtain the product of $2, 4y, 8y^2, 16y^3$
Answer$2 \times 4 y \times 8 y^{2} \times 16 y^{3}$
= $(2 \times 4 \times 8 \times 16)\left(y \times y^{2} \times y^{3}\right)$
$= 1024y^6$
View full question & answer→Question 231 Mark
Obtain the product of $a, - a^2$ and $a^3$
AnswerProduct of $a \times$ $(- a^2)$$\times$ $a^3= - a^6$
View full question & answer→Question 241 Mark
Obtain the volume of rectangular box with the length, breadth and height respectively: $a, 2b, 3c.$
AnswerVolume of the rectangular box
$=$ Length $\times$ Breadth $\times$ Height
$= (a) \times (2b) \times (3c)$
$= (2 \times 3) \times (a \times b \times c)$
$= 6abc$
View full question & answer→Question 251 Mark
Obtain the volume of rectangular box with the length, breadth and height respectively: $2p, 4q, 8r$
AnswerVolume of the rectangular box
$=$ Length $\times$ Breadth $\times$ Height
$= (2p) \times (4q) \times (8r)$
$= (2 \times 4 \times 8) \times (p \times q \times r)$
$= 64pqr$
View full question & answer→Question 261 Mark
Find the areas of rectangles with the monomials as their lengths and breadths respectively: $(10m, 5n)$
AnswerArea of the rectangle
$=$ Length $\times$ Breadth
$= (10m) \times(5n)$
$= (10 \times 5) \times(m \times n)$
$= 50 \times(mn)$
$= 50mn$
View full question & answer→Question 271 Mark
Find the areas of rectangle with the monomials as their lengths and breadths respectively: $(p, q)$
AnswerArea of the rectangle
$=$ Length $\times$ Breadth
$= p \times q$
$= pq$
View full question & answer→Question 281 Mark
Find the product of $4p, 0$
Answer$(4p) \times 0$
$= (4 \times 0) \times p$
$= 0 \times p$
$= 0$
View full question & answer→Question 291 Mark
Find the product of $4p^3, – 3p$
Answer$(4p^3) \times (– 3p)$
$= \{4 \times (– 3)\} \times (p^3 \times p)$
$= (– 12) \times p^4$
$= –12p^4$
View full question & answer→Question 301 Mark
Find the product of $– 4p, 7pq$
Answer$(– 4p) \times (7pq)$
$= \{(– 4) \times 7\} \times \{p \times (pq)\}$
$= (–28) \times (p \times p \times q)$
$= (–28) \times (p^2q)$
$= –28p^2q$
View full question & answer→Question 311 Mark
Find the product of $–4p, 7p.$
Answer$(– 4p) \times (7p)$
$= \{(– 4) \times 7\} \times (p \times p)$
$= (– 28) \times p^2$
$= – 28p^2$
View full question & answer→Question 321 Mark
Find the product of $4, 7p.$
Answer$4 \times 7p$
$= (4 \times 7) \times p$
$= 28 \times p$
$= 28p$
View full question & answer→Question 331 Mark
Add the following expressions: $l^2+ m^2, m^2+ n^2, n^2+ l^2, 2lm + 2mn + 2nl$
AnswerWriting the four given expressions in separate rows, with like terms one below the other, we have
Hence the sum is $2(l^2+ m^2+ n^2+ lm + mn + nl).$ View full question & answer→Question 341 Mark
Add: $2 p^2 q^2-3 p q+4,5+7 p q-3 p^2 q^2$
View full question & answer→Question 351 Mark
Add: $a – b + ab, b – c + bc, c – a + ac.$
View full question & answer→Question 361 Mark
Add: $ab - bc, bc - ca, ca - ab$
View full question & answer→Question 371 Mark
Multiply: $\left(a^2+2 b^2\right)$ and $(5a – 3b)$
Answer$\left(a^2+2 b^2\right) \times(5 a-3 b)=a^2(5 a-3 b)+2 b^2(5 a-3 b)$
$=5 a^3-3 a^2 b+10 a b^2-6 b^3$
View full question & answer→Question 381 Mark
Multiply: $(a + 7)$ and $(b – 5)$
Answer$(a + 7) × (b – 5)$
$= a × (b – 5) + 7 × (b – 5)$
$= ab - 5a + 7b - 35$
View full question & answer→Question 391 Mark
Multiply : $(x - y)$ and $(3x + 5y)$
Answer$(x – y) × (3x + 5y) = x × (3x + 5y) – y × (3x + 5y)$
= $(x × 3x) + (x × 5y) – (y × 3x) – ( y × 5y) $
= $3x^{2} + 5xy – 3yx – 5y^{2}$ = $3x^{2} + 2xy – 5y^{2}$
View full question & answer→Question 401 Mark
Multiply: $(x - 4)$ and $(2x + 3)$
Answer$(x – 4) × (2x + 3) = x × (2x + 3) – 4 × (2x + 3)$
$= (x × 2x) + (x × 3) – (4 × 2x) – (4 × 3)$
$= 2x^{2} + 3x – 8x – 12 = 2x^2– 5x – 12$
View full question & answer→Question 411 Mark
Add: $5m(3 – m)$ and $6m^2– 13m$
AnswerFirst expression $= 5m(3 – m) = (5m \times 3) – (5m \times m) = 15m – 5m^2$
Now adding the second expression to it, $15m – 5m^2+ 6m^2– 13m = m^2+ 2m$
View full question & answer→Question 421 Mark
Simplify the expression and evaluate as directed: $x(x - 3) + 2$ for $x = 1$
Answer$x(x – 3) + 2 = x^2- 3x + 2$
For $x = 1,$
$x^2- 3x + 2 = (1)^2- 3(1) + 2$
$= 1 - 3 + 2 = 3 - 3 = 0$
View full question & answer→