[2 Mark Question Answer]

Question 12 Marks

Factorise the following by the difference of two squares$:(x - 2y)^2 -z^2$

Answer

$(x - 2y)^2 - z^2$
$= (x - 2y)^2 - (z)^2$
$= (x - 2y - z)(x - 2y + z).$

View full question & answer→

Question 22 Marks

Factorise the following by the difference of two squares$:(x + y)^2 -1$

Answer

$(x + y)^2 - 1$
$= (x + y)^2 - (1)^2$
$= (x + y + 1)(x + y - 1).$

View full question & answer→

Question 32 Marks

Factorise the following by the difference of two squares$:m ^2-\frac{1}{9} n ^2$

Answer

$m^2-\frac{1}{9} n^2$
$ =m^2-\left(\frac{1}{3} n\right)^2$
$ =\left(m-\frac{1}{3} n\right)\left(m+\frac{1}{3} n\right) .$

View full question & answer→

Question 42 Marks

Factorise the following by the difference of two squares$:625 - b^2$

Answer

$625 - b^2$
$= (25)^2 (b)^2$
$= (25 - b)(25 + b)$

View full question & answer→

Question 52 Marks

Factorise the following by the difference of two squares$:x^6 - 196$

Answer

$x^6 - 196$
$= (x^3)^2 - (14)^2$
$= (x^3 - 14)(x^3 + 14).$

View full question & answer→

Question 62 Marks

Factorise the following by the difference of two squares$:64x^2 - 121y^2$

Answer

$64x^2 - 121y^2$
$= (8x)^2 - (1y)^2$
$= (8x - 11y)(8x + 11y).$

View full question & answer→

Question 72 Marks

Factorise the following by the difference of two squares$:x^2 - 16$

Answer

$x^2 - 16$
$= x^2 - 4^2$
$= (x - 4)(x + 4).$

View full question & answer→

Question 82 Marks

Factorise the following by grouping the terms$:x + y + m(x + y)$

Answer

$x + y + m(x + y)$
$= (x + y) + m(x + y)$
$= (x + y)(1 + m).$

View full question & answer→

Question 92 Marks

Factorise the following by grouping the term$s:x^2 - (p + q)x + pq$

Answer

$x^2 - (p + q)x + pq$
$= x^2 - px - qx + pq$
$= (x^2 - px) - (qx + pq)$
$= x(x - p) - q(x - p)$
$= (x - p)(x - q).$

View full question & answer→

Question 102 Marks

Factorise the following by grouping the terms$:8x^3 - 24x^2y + 54xy^2 -162y^3$

Answer

$8x^3 - 24x^2y + 54xy^2 - 162y^3$
$= (8x^3 - 24x^2y) + (54xy^2 - 62y^3)$
$= 8x^2(x - 3y) + 54y^2(x - 3y)$
$= (x - 3y)(8x^2 + 54y^2).$

View full question & answer→

Question 112 Marks

Factorise the following by grouping the terms$:x(x - 4)- x + 4$

Answer

$x(x - 4) - x + 4$
$= x(x - 4) - 1(x - 4)$
$= (x - 4)(x - 1).$

View full question & answer→

Question 122 Marks

Factorise the following by grouping the terms$:15xy - 9x - 25y + 15$

Answer

$15xy - 9x - 25y + 15$
$= (15xy - 9x) - (25y + 15)$
$= 3x(5y - 3) - 5(5y - 3)$
$= (5y - 3)(3x - 5).$

View full question & answer→

MATHEMATICS [2 Mark Question Answer]

Test yourself on this topic