2 Marks Questions

Questions · Page 2 of 2

Question 512 Marks

Find the following products: $(x + 4)(x + 7)$

Answer

Here, we will use the identity $(x + a)(x + b) = x^2+ (a + b)x + ab.$
$(x + 4)(x + 7)$
$ =x^2+(4+7) x+4 \times 7 $
$ =x^2+11 x+28 $

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Question 522 Marks

Simplify:
$ a^2 b\left(a^3-a+1\right)-a b\left(a^4-2 a^2+2 a\right)-b\left(a^3-a^2-1\right) $

Answer

To simplify, we will use distributive law as follows:
$ a^2 b\left(a^3-a+1\right)-a b\left(a^4-2 a^2+2 a\right)-b\left(a^3-a^2-1\right) $
$ =a^5 b-a^3 b+a^2 b-a^5 b+2 a^3 b-2 a^2 b-a^3 b+a^2 b+b $
$ =a^5 b-a^5 b-a^3 b+2 a^3 b-a^3 b+a^2 b-2 a^2 b+a^2 b+b $
$ =b $

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Question 532 Marks

Using the formula for squaring a binomial, evaluate the following: $(1001)^2$

Answer

Here, we will use the identity $(a + b)^2= a^2+ 2ab + b^2$.
$ (1001)^2 $
$ =(1000+1)^2 $
$ =(1000)^2+2 \times 1000 \times 1+1^2 $
$ =1000000+2000+1 $
$ =1002001 $

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Question 542 Marks

Simplify the following using the formula $(a + b)^2= a^2+ 2ab + b^2:$
$(82)^2-(18)^2$

Answer

Here, we will use the identity $(a - b) (a + b) = a^2- b^2$
Let us consider the following expression:
$(82)^2-(18)^2$
$= (82 + 18)(82 - 18)$
$= 100 × 64$
$= 6400$

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Question 552 Marks

Evaluate the following:
$109 × 107$

Answer

Here, we will use the identity $(x + a)(x + b) = x^2+ (a + b)x + ab.$
$109 × 107$
$= (100 + 9)(100 + 7)$
$= 100^2+ (9 + 7)100 + 9 × 7$
$= 10000 + 1600 + 63$
$= 11663$

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Question 562 Marks

Find the following products: $(x + 7)(x - 5)$

Answer

Here, we will use the identity $(x + a)(x - b) = x^2+ (a - b)x - ab.$
$(x + 7)(x - 5)$
$= x^2+ (7 - 5)x - 7 × 5$
$= x^2+ 2x - 35$

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Question 572 Marks

Using the formula for squaring a binomial, evaluate the following: $(102)^2$

Answer

Here, we will use the identity $(a + b)^2= a^2+ 2ab + b^2$.
$ (102)^2 $
$=(100+2)^2 $
$ =(100)^2+2 \times 100 \times 2+2^2 $
$ =10000+400+4 $
$ =10404 $

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Question 582 Marks

Find the following products: $\big(\text{y}^2+\frac{5}{7}\big)\big(\text{y}^2−\frac{14}{5}\big)$

Answer

Here, we will use the identity $(x+a)(x-b)=x^2+(a-b) x-a b$.
$\big(\text{y}^2+\frac{5}{7}\big)\big(\text{y}^2−\frac{14}{5}\big)$
$=\big(\text{y}^2)^2+\big(\frac{5}{7}−\frac{14}{5}\big)\big(\text{y}^2\big)−\frac{5}{7}×\frac{14}{5}$
$=\text{y}^4−\frac{73}{35}\text{y}^2−2$

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Question 592 Marks

Using the formula for squaring a binomial, evaluate the following: $(703)^2$

Answer

Here, we will use the identity $(a + b)^2= a^2+ 2ab + b^2$.
$(703)^2$
$= (700 + 3)^2$
$= (700)^2+ 2 × 700 × 3 + 3^2$
$= 490000 + 4200 + 9$
$= 494209$

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Question 602 Marks

Evaluate the following: $35 \times 37$

Answer

Here, we will use the identity $(x + a)(x + b) = x^2+ (a + b)x + ab.$
$35 × 37$
$= (30 + 5) (30 + 7)$
$= 30^2+ (5 + 7) 30 + 5 × 7$
$= 900 + 360 + 35$
$= 1295$

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Question 612 Marks

Simplify:
$a(b - c) + b(c - a) + c(a - b)$

Answer

To simplify, we will use distributive law as follows:
$a(b - c) + b(c - a) + c(a - b)$
$= ab - ac+ bc - ba + ca - cb$
$= ab - ba - ac + ca + bc - cb$
$= 0$

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Question 622 Marks

Using the formula for squaring a binomial, evaluate the following: $(99)^2$

Answer

Here, we will use the identity $(a + b)^2= a^2+ 2ab + b^2$.
$(99)^2 $
$ =(100-1)^2 $
$ =(100)^2-2 \times 100 \times 1+1^2 $
$ =10000-200+1$
$ =9801 $

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MATHS 2 Marks Questions

2 Marks Questions