Question 12 Marks
Divide $: 6m^2 − 16m^3 + 10m^4$ by $− 2m$
Answer$6 m^2-16 m^3+10 m^4 \text { by }-2 m$
$=\frac{6 m^2-16 m^3+10 m^4}{-2 m}$
$=\frac{6 m^2}{-2 m}-\frac{6 m^3}{-2 m}+\frac{10 m^4}{-2 m}$
$=-3 m^{2-1}+8 m^{3-1}-5 m^{4-1}$
$=-3 m+8 m^2-5 m^3$
View full question & answer→Question 22 Marks
Divide $: 9x^3 − 6x^2$ by $3x$
Answer$9 x^3-6 x^2 \text { by } 3 x$
$=\frac{9 x^3-6 x^2}{3 x}$
$=\frac{9 x^3}{3 x}-\frac{6 x^2}{3 x}$
$=3 x^{3-1}-2 x^{2-1}$
$=3 x^2-2 x$
View full question & answer→Question 32 Marks
Simplify : $\frac{-24 x^6 y^2}{6 x^6 y}$
Answer$\frac{-24 x^6 y^2}{6 x^6 y}$
$=\frac{-4 \times 6 \times x^6 \times y^2}{6 \times x^6 \times y}$
$=-4 y^{2-1}$
$=-4 y$
View full question & answer→Question 42 Marks
Simplify : $\frac{35 x^4 y^2}{-15 x^2 y^2}$
Answer$\frac{35 x^4 y^2}{-15 x^2 y^2}$
$=\frac{-5 \times-7 \times x^4 \times y^2}{3 \times-5 \times x^2 \times y^2}$
$=\frac{-7 x^{4-2}}{3}$
$=-\frac{7 x^2}{3}$
View full question & answer→Question 52 Marks
Divide: $\frac{64 x^2 y^2}{z^2}$ by $\frac{8 x y}{z}$
Answer$\frac{64 x^2 y^2}{z^2} \div \frac{8 x y}{z}$
$=\frac{8 \times 8 \times x^2 \times y^2}{z^2} \times \frac{z}{8 \times x \times y}$
$=\frac{8 x^{2-1} y^{2-1}}{z^{2-1}}$
$=\frac{8 x y}{z}$
View full question & answer→Question 62 Marks
Divide : $\frac{-5.5 x^2}{y} \text { by } \frac{11 x}{y}$
Answer$\frac{-5.5 x^2}{y} \div \frac{11 x}{y}$
$=\frac{-55 x^2}{10 y} \times \frac{y}{11 x}$
$=-\frac{5 x}{10}$
$=-0.5 x$
View full question & answer→Question 72 Marks
Divide: $\frac{2 a ^2}{9 b ^2}$ by $\frac{3 b }{2 a }$
Answer$\frac{2 a ^2}{9 b ^2} \div \frac{3 b }{2 a }$
$=\frac{2 a ^2}{9 b ^2} \times \frac{2 a }{3 b }$
$=\frac{2 \times 2 \times a ^{2+1}}{9 \times 3 b ^{2+1}}$
$=\frac{4 a ^3}{27 b ^3}$
View full question & answer→Question 82 Marks
Divide $: 20x^3a^6$ by $5xy$
Answer$20 x^3 a^6 \div 5 x y$
$=\frac{4 \times 5 x^3 a^6}{5 x y}$
$=\frac{4 \times 5 \times x^{3-1} \times a^6}{5 x y}$
$=\frac{4 x^2 a^6}{y}$
View full question & answer→Question 92 Marks
Divide $: − 15p^6q^8$ by $− 5p^6q^7$
Answer$-15 p^6 q^8 \div-5 p^6 q^7$
$=\frac{-5 \times 3 \times p^6 \times q^8}{-5 \times p^6 \times q^7}$
$=3 q^{8-7}$
$=3 q$
View full question & answer→Question 102 Marks
Simplify $: − 64x^4y^3z \div 4x^3y^2z$
Answer$-64 x^4 y^3 z \div 4 x^3 y^2 z$
$=\frac{4 \times 4 \times 4 \times x^4 \times y^3 \times z}{4 \times x^3 \times y^2 \times z}$
$=-16 x^{4-3} \times y^{3-2}$
$=-16 x y$
View full question & answer→Question 112 Marks
Simplify $: 40p^3q^4r^5 \div 10p^3q$
Answer$40 p^3 q^4 r^5 \div 10 p^3 q$
$=\frac{4 \times 10 \times p^{3-3} \cdot q^{4-1} \cdot r^5}{10}$
$=4 \times q^{4-1} \times r^5$
$=4 q^3 r^5$
View full question & answer→Question 122 Marks
Find the product of $5x − 6y − 7z$ and $2x + 3y$
Answer$(5x − 6y − 7z) \times (2x + 3y)$
$= 2x \times (5x − 6y − 7z) + 3y \times (5x − 6y − 7z)$
$= 10x^2 − 12xy − 14xz + 15xy − 18y^2 − 21yz$
$= 10x^2 + 3xy − 14xz − 18y^2 − 21yz$
View full question & answer→Question 132 Marks
Find the product of $2abc − 3xy$ and $2abc + 3xy$
Answer$(2abc − 3xy) \times (2abc + 3xy)$
$= 2abc \times (2abc − 3xy) + 3xy \times (2abc − 3xy)$
$= 4a^2b^2c^2− 6abcxy + 6abcxy − 9x^2y^2$
$= 4a^2b^2c^2 − 9x^2y^2$
View full question & answer→Question 142 Marks
Find the product of $xy − ab$ and $xy + ab$
Answer$(xy − ab) \times (xy + ab)$
$= xy \times (xy − ab) + ab (xy − ab)$
$= x^2y^2 − abxy + abxy − a^2b^2$
$= x^2y^2 − a^2b^2$
View full question & answer→Question 152 Marks
Multiply $: (2x + 5y)$ and $(2x + 5y)$
Answer$(2x + 5y) \times (2x + 5y)$
$= 2x \times (2x + 5y) + 5y \times (2x + 5y)$
$= 4x^2+ 10xy + 10xy + 25y^2$
$= 4x^2+ 20xy + 25y^2$
View full question & answer→Question 162 Marks
Multiply $: (x + 9y)$ and $(x – 5y)$
Answer$(x + 9y) \times (x − 5y)$
$= x \times (x + 9y) − 5y (x + 9y)$
$= x^2 + 9xy − 5xy − 45y^2$
$= x^2 + 4xy − 45y^2$
View full question & answer→Question 172 Marks
Multiply $: (3x – 5y)$ and $(x + 6y)$
Answer$(3x − 5y) \times (x + 6y)$
$= x \times (3x − 5y) + 6y (3x − 5y)$
$= 3x^2 − 5xy + 18xy − 30y^2$
$= 3x^2 + 13xy − 30y^2$
View full question & answer→Question 182 Marks
Multiply $: 2x + y$ and $x + 3y$
Answer$(2x + y) \times (x + 3y)$
$= x \times (2x + y) + 3y \times (2x + y)$
$= 2x^2 + xy + 6xy + 3y^2$
$= 2x^2 + 7xy + 3y^2$
View full question & answer→Question 192 Marks
Multiply $: x – 5$ and $x – 3$
Answer$(x − 5) \times (x − 3)$
$= x \times (x − 5) − 3 \times (x − 5)$
$= x^2 − 5x − 3x + 15$
$= x^2 − 8x + 15$
View full question & answer→Question 202 Marks
Multiply $: x – 5$ and $x + 3$
Answer$(x − 5) \times (x + 3)$
$= x \times (x − 5 ) + 3 \times (x − 5)$
$= x^2 + 5x − 3x − 15$
$= x^2 − 2x − 15$
View full question & answer→Question 212 Marks
Multiply $: x + 5$ and $x – 3$
Answer$(x + 5) \times (x − 3)$
$= x \times (x + 5) − 3 \times (x + 5)$
$= x^2+ 5x − 3x − 15$
$= x^2 + 2x − 15$
View full question & answer→Question 222 Marks
Multiply $: x + 2$ and $x + 10$
Answer$(x + 2) \times (x + 10)$
$= x \times (x + 2) + 10 \times (x + 2)$
$= x^2+ 2x + 10x + 20$
$= x^2 + 12x + 20$
View full question & answer→Question 232 Marks
Multiply $: xy − yz$ and $x^2yz^2$
Answer$xy − yz \times x^2yz^2$
$= xy \times x^2yz^2 − yz \times x^2yz^2$
$= x^{2+1} \times y^{1+1} \times z^2 − x^2 \times y^{1+1} \times z^{2+1}$
$= x^3y^2z^2 − x^2y^2z^3$
View full question & answer→Question 242 Marks
Multiply $: 9xy^2 + 3x^2y$ by $5xy$
Answer$(9xy^2 + 3x^2y) \times 5xy$
$= 9xy^2 \times 5xy + 3x^2y \times 5xy$
$= 45x^2y^3 + 15x^3y^2$
View full question & answer→Question 252 Marks
Multiply $: 3ab − 4b$ by $3ab$
Answer$(3ab − 4b) \times 3ab$
$= 3ab \times 3ab − 4b \times 3ab$
$= 3 \times 3a^{1+1}\times b^{1+1} − 4 \times 3 \times a \times b^{1+1}$
$= 9a^2b^2 − 12ab^2$
View full question & answer→Question 262 Marks
Subtract x – 2y – z from the sum of 3x – y + z and x + y – 3z.
Answer(3x – y + z) + (x + y – 3z) – (x – 2y – z)
= 3x – y + z + x + y – 3z – x + 2y + z
= 3x + x – x – y + y + 2y + z + z – 3z
= 3x + 2y – z
View full question & answer→Question 272 Marks
From the sum of 3a – 2b + 4c and 3b – 2c subtract a – b – c.
Answer(3a – 2b + 4c) + (3b – 2c) – (a – b – c)
= 3a – 2b + 4c + 3b – 2c – a + b + c
= 3a – a + 3b + b – 2b + 4c + c – 2c
= 2a + 2b + 3c
View full question & answer→Question 282 Marks
From the sum of x + y – 2z and 2x – y + z subtract x + y + z.
Answer(x + y − 2z) + (2x − y + z) − (x + y + z)
= x + y − 2z + 2x − y + z − x − y − z
= x + 2x − x + y − y − y − 2z − z + z
= 2x − y − 2z
View full question & answer→Question 292 Marks
Take $1 − a + a^2$ from $a^2 + a + 1.$
Answer$(a^2 + a + 1) − (1 − a + a^2)$
$= a^2 + a + 1 − 1 + a − a^2$
$= a^2 − a^2 + a + a + 1 − 1$
$= 2a$
View full question & answer→Question 302 Marks
Take 5x + 6y − 3z from 3x + 5y − 4z.
Answer(3x + 5y − 4z) − (5x + 6y − 3z)
= 3x + 5y − 4z − 5x − 6y + 3z
= 3x − 5x + 5y − 6y − 4z + 3z
= − 2x − y − z
View full question & answer→Question 312 Marks
Take − ab + bc − ca from bc − ca + ab.
Answer(bc − ca + ab) − (− ab + bc − ca)
= bc − ca + ab + ab − bc + ca
= bc − bc − ca + ca + ab + ab
= 2ab
View full question & answer→Question 322 Marks
Subtract:
2ab + cd − ac − 2bd from ab − 2cd + 2ac + bd.
Answer(ab − 2cd + 2ac + bd) − (2ab + cd − ac − 2bd)
= ab − 2cd + 2ac + bd − 2ab − cd + ac + 2bd
= ab − 2ab − 2cd − cd + 2ac + ac + bd + 2bd
= − ab − 3cd + 3ac + 3bd
View full question & answer→Question 332 Marks
Subtract:
− 8x − 12y + 17z from x − y − z.
Answer(x − y − z) − (− 8x − 12y + 17z)
= x − y − z + 8x + 12y − 17z
= x + 8x + 12y − y − z − 17z
= 9x + 11y − 18z
View full question & answer→Question 342 Marks
Subtract:
5 − a − 4b + 4c from 5a − 7b + 2c.
Answer(5a − 7b + 2c) − (5 − a − 4b + 4c)
= 5a − 7b + 2c − 5 + a + 4b − 4c
= 5a + a − 7b + 4b + 2c − 4c − 5
= 6a − 3b − 2c − 5
View full question & answer→Question 352 Marks
Subtract:
4x − 6y + 3z from 12x + 7y − 21z.
Answer(12x + 7y − 21z) − (4x − 6y + 3z)
= 12x + 7y − 21z − 4x + 6y − 3z
= 12x − 4x + 7y + 6y − 21z − 3z
= 8x + 13y − 24z
View full question & answer→Question 362 Marks
Subtract:
5a − 3b + 2c from a − 4b − 2c.
Answer(a − 4b − 2c) − (5a − 3b + 2c)
= a − 4b − 2c − 5a + 3b − 2c
= a − 5a − 4b + 3b − 2c − 2c
= − 4a − b − 4c
View full question & answer→Question 372 Marks
Evaluate:
(6y − 13) − (4 − 7y)
Answer(6y − 13) − (4 − 7y)
= 6y − 13 − 4 + 7y
= 6y + 7y − 13 − 4
= 13y − 17
View full question & answer→Question 382 Marks
Answer7 − (4a − 5)
= 7 − 4a + 5
= 7 + 5 − 4a
= 12 − 4a
View full question & answer→Question 392 Marks
Evaluate:
(8x + 7y) − (4y − 3x)
Answer(8x + 7y) − (4y − 3x)
= 8x + 7y − 4y + 3x
= 8x + 3x + 7y − 4y
= 11x + 3y
View full question & answer→Question 402 Marks
Evaluate:
(8a + 15b) − (3b − 7a)
Answer(8a + 15b) − (3b − 7a)
= 8a + 15b − 3b + 7a
= 8a + 7a + 15b − 3b
= 15a + 12b
View full question & answer→Question 412 Marks
Evaluate:
(5x − 3y) − (x + y)
Answer(5x − 3y) − (x + y)
= 5x − 3y − x − y
= 5x − x − 3y − y
= 4x − 4y
= 4 (x − y)
View full question & answer→Question 422 Marks
Answer3a − (a + 2b)
= 3a − a − 2b
= 2a − 2b
= 2 (a − b)
View full question & answer→Question 432 Marks
Add the following expression:
$a^3 − 2b^3 + a, b^3 − 2a^3 + b$ and $− 2b + 2b^3 − 5a + 4a^3$
Answer$(a^3 − 2b^3 + a) + (b^3 − 2a^3 + b) + (− 2b + 2b^3 − 5a + 4a^3)$
$= a^3− 2b^3 + a + b^3 − 2a^3 + b − 2b + 2b^3 − 5a + 4a^3$
$= a^3 + 4a^3 − 2a^3 − 2b^3+ b^3 + 2b^3 + a − 5a + b − 2b$
$= 3a^3 + b^3 − 4a − b$
View full question & answer→Question 442 Marks
Add the following expression:
$− x^2 − 3xy + 3y^2 + 8, 3x^2− 5y^2− 3 + 4xy$ and $− 6xy + 2x^2− 2 + y^2$
Answer$(− x^2 − 3xy + 3y^2 + 8) + (3x^2 − 5y^2 − 3 + 4xy) + (− 6xy + 2x^2 − 2 + y^2)$
$= − x^2 − 3xy + 3y^2+ 8 + 3x^2 − 5y^2− 3 + 4xy − 6xy + 2x^2 − 2 + y^2$
$= − x^2 + 3x^2 + 2x^2 − 3xy − 6xy + 4xy + 3y^2 + y^2 − 5y^2 + 8 − 3 − 2$
$= 4x^2 − 5xy − y^2 + 3$
View full question & answer→Question 452 Marks
Add the following expression:
$− 17x^2 − 2xy + 23y^2, − 9y^2 + 15x^2 + 7xy$ and $13x^2 + 3y^2 − 4xy$
Answer$(− 17x^2 − 2xy + 23y^2) + (− 9y^2 + 15x^2 + 7xy) + (13x^2+ 3y^2 − 4xy)$
$= − 17x^2 − 2xy + 23y^2 − 9y^2 + 15x^2 + 7xy + 13x^2 + 3y^2 − 4xy$
$= − 17x^2 + 15x^2+ 13x^2 − 2xy − 4xy + 7xy + 23y^2 + 3y^2 − 9y^2$
$= 11x^2 + xy + 17y^2$
View full question & answer→Question 462 Marks
The sum of two expressions is $3a^2 + 2ab – b^2.$ If one of them is $2a^2 + 3b^2,$ find the other.
Answer$(3a^2 + 2ab − b^2) − (2a^2 + 3b^2)$
$= 3a^2 + 2ab − b^2 − 2a^2 − 3b^2$
$= 3a^2 − 2a^2 + 2ab − b^2 − 3b^2$
$= a^2+ 2ab − 4b^2$
View full question & answer→Question 472 Marks
The sum of two expressions is $5x^2 – 3y^2.$ If one of them is $3x^2 + 4xy – y^2,$ find the other.
Answer$(5x^2 − 3y^2) − (3x^2 + 4xy − y^2)$
$= 5x^2 − 3y^2− 3x^2 − 4xy + y^2$
$= 5x^2 − 3x^2− 4xy − 3y^2 + y^2$
$= 2x^2 − 4xy − 2y^2$
View full question & answer→Question 482 Marks
Simplify:
2.5a + 4.6b + 1.2a − 3.6b
Answer2.5a + 4.6b + 1.2a − 3.6b
= 2.5a + 1.2a + 4.6b − 3.6b
= 3.7a + b
View full question & answer→Question 492 Marks
Simplify:
6.4a + 5.3b − 2.4a − 2.2b
Answer6.4a + 5.3b − 2.4a − 2.2b
= 6.4a − 2.4a + 5.3b − 2.2b
= 4a + 3.1b
View full question & answer→Question 502 Marks
Simplify: $6x^2y − 2xy^2 + 5x^2y − xy^2$
Answer$6x^2y − 2xy^2 + 5x^2y − xy^2$
$= 6x^2y + 5x^2y − 2xy^2 − xy^2$
$= 11x^2y − 3xy^2$
View full question & answer→