2 Marks Questions

Question 2012 Marks

Write the greatest common factor in each of the following terms. $qrxy, pryz, rxyz$

Answer

$qrxy, pryz, rxyz qrxy$
$= q × r × x × y pryz$
$= p × r × y × z rxyz$
$= r × x × y × z GCF = ry$

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Question 2022 Marks

Factorise the following, using the identity $a^2- 2ab + b^2= (a - b)^2$.
$x^2- 8x + 16$

Answer

$ x^2-8 x+16 $
$ =x^2-2 \times x \times 4+4^2 $
$ =(x-4)^2 $
$ =(x-4)(x-4) $

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Question 2032 Marks

Factorise the following, using the identity $a^2+2 a b+b^2=(a+b)^2 $
$a^2 x^2+2 a b x+b^2$

Answer

$a^2 x^2+2 a b x+b^2$
$=(a x)^2+2 \times a x \times b+b^2$
$=(a x+b)^2$
$=(a x+b)(a x+b)$

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Question 2042 Marks

Factorise the following, using the identity $a^2-2 a b+b^2=(a-b)^2 .$
$a^2 y^2-2 a b y+b^2$

Answer

$a^2 y^2-2 a b y+b^2$
$(a y)^2-2 \times a y \times b+b^2$
$(a y-b)^2$
$=(a y-b)(a y-b)$

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Question 2052 Marks

Factorise the following. $y^2+ 18x + 65$

Answer

$y^2+18 x+65$
$=y^2+13 y+15 y+5 \times 13$
$=y(y+13)+5(y+13)$
$=(y+13)(y+5)$

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Question 2062 Marks

Add: $7 a^2 b c,-3 a b c^2, 3 a^2 b c, 2 a b c^2$

Answer

We have,
$7 a^2 b c,-3 a b c^2, 3 a^2 b c, 2 a b c^2$
$=7 a^2 b c-3 a b c^2+3 a^2 b c+2 a b c^2$
$=10 a^2 b c+(-a b c)^2$
$=10 a^2 b c-a b c^2$

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Question 2072 Marks

Using suitable identities, evaluate the following. $(339)^2- (161)^2$

Answer

$(339)^2-(161)^2$
$=(339+161)(339-161)$
$=500 \times 178$
$=89000$

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Question 2082 Marks

Write the greatest common factor in each of the following terms.
$63 p^2 a^2 r^2 s,-9 p q^2 r^2 s^2, 15 p^2 q r^2 s^2,-60 p^2 a^2 r s^2$

Answer

$63 p^2 a^2 r^2 s,-9 p q^2 r^2 s^2, 15 p^2 q r^2 s^2,-60 p^2 a^2 r s^2$
$63 p^2 a^2 r^2 s = 3 × 3 × 7 × p × p × a × a × r × r × r$
$-9 p q^2 r^2 s^2= -3 × 3 × p × q × q × r × r × s × s$
$15 p^2 q r^2 s^2= 3 × 5 × p × p × q × r × r × s × s × s$
$-60 p^2 a^2 r s^2= 2 × 2 × 3 × 5 × p × p × a × a × r × s × s$
$GCF = 3prs$

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Question 2092 Marks

Factorise the following, using the identity $a^2+ 2ab + b^2= (a + b)^2$
$ 4 x^4+12 x^3+9 x^2 $

Answer

$ 4 x^4+12 x^3+9 x^2 $
$=x^2\left(4 x^2+12 x+9\right) $
$ =x^2\left[(2 x)+2 \times 2 x \times 3+3^2\right] $
$ =x^2(2 x+3)^2 $
$ =x^2(2 x+3)(2 x+3) $

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Question 2102 Marks

Factorise the following, using the identity $a^2+ 2ab + b^2= (a + b)^2$
$9\text{x}^2+2\text{xy}+\frac{\text{y}^2}{9}$

Answer

$9\text{x}^2+2\text{xy}+\frac{\text{y}^2}{9}$$=(3\text{x})^2+2\times3\text{x}\times\frac{\text{y}}{3}+\Big(\frac{\text{y}}{3}\Big)^2$
$=\Big(3\text{x}+\frac{\text{y}}{3}\Big)^2$
$=\Big(3\text{x}+\frac{\text{y}}{3}\Big)\Big(3\text{x}+\frac{\text{y}}{3}\Big)$

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Question 2112 Marks

Multiply the following: $(ab + c), (ab + c)$

Answer

$(ab + c), (ab + c)$
$(ab + c)(ab + c)$
$= ab(ab + c) + c(ab + c)$
$= a^2b^2+ abc + cab + c^2$
$= a^2b^2+ 2abc + c^2$

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Question 2122 Marks

Using suitable identities, evaluate the following.
$(9.7)^2- (0.3)^2$

Answer

$(9.7)^2- (0.3)^2$
$= (9.7 + 0.3)(9.7 - 0.3)$
$= 10 \times 9.4$
$= 94$

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Question 2132 Marks

Factorise the following, using the identity $a^2- 2ab + b^2= (a - b)^2$.
$4y^2- 12y + 9$

Answer

$4 y^2-12 y+9$
$=(2 y)^2-2 \times 2 y \times 3+3^2$
$=(2 y-3)^2$
$=(2 y-3)(2 y-3)$

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Question 2142 Marks

Factorise the following using the identity $a^2- b^2= (a + b)(a - b).$
$\frac{2\text{p}^2}{25}-32\text{q}^2$

Answer

$\frac{2\text{p}^2}{25}-32\text{q}^2$$= 2\Big(\frac{\text{p}^2}{25}-16\text{q}^2\Big)$
$=2\Big[\Big(\frac{\text{p}^2}{5}\Big)-\big(4\text{q}^2\big)\Big]$
$=2\Big(\frac{\text{p}}{5}+4\text{q}\Big)\Big(\frac{\text{p}}{5}-4\text{q}\Big)$

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MATHS 2 Marks Questions