Algebra - Factorising By Grouping

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Question 1

Expand the following

a) $(a+b)(x+y)$a s v d
b) $(a+2)(b+3)$a s v d
c) $(x+5)(x+8)$a s v d
d) $(x^2+x)(x+10)$a s v d
e) $(a-x)(b+y)$a s v d
f) $(x-6)(y-9)$a s v d

Question 2

Factorise the following by grouping (in pairs)

a) $px+py+qx+qy$a s v d
b) $sp+sq+tp+tq$a s v d
c) $ab+5a+3b+15$a s v d
d) $xy+10x+6y+60$a s v d
e) $x^2+8x+3x+24$a s v d
f) $y^2+7y+5y+35$a s v d

Question 3

Factorise the following by grouping (in pairs)

a) $ax+ay-bx-by$a s v d
b) $hm+hn-5m-5n$a s v d
c) $cx-2c+dx-2d$a s v d
d) $py-pz+2y-2z$a s v d
e) $x^2+7x-2x-14$a s v d
f) $x^2-x+7x-7$a s v d

Question 4

Factorise the following by grouping (in pairs)

a) $ac-ad-bc+bd$a s v d
b) $hx-2x-hy+2y$a s v d
c) $xy-x^2-6y+6x$a s v d
d) $5v^2-hv^2-5w+hw$a s v d
e) $x^2-4x-6x+24$a s v d
f) $z^2-8z-z+8$a s v d

Question 5

Factorise the following by grouping (in pairs)

a) $xy-2x+5y-10$a s v d
b) $px-py-qx+qy$a s v d
c) $3x^2+15x+4x+20$a s v d
d) $2x^2+12x-5x-30$a s v d
e) $4ap-4bp+5a-5b$a s v d
f) $5t^2-5t-6t+6$a s v d
g) $6xy-3x-8y+4$a s v d
h) $40z^2-8z-5z+1$a s v d

Question 6

Factorise the following by grouping (in pairs)

a) $20pq+24p+15q+18$a s v d
b) $9t^3+27t^2-7t-21$a s v d
c) $4x+12-x^3-3x^2$a s v d
d) $2x^3-9x^2-8x+36$a s v d
e) $3x^4-15x^2+x^2-5$a s v d
f) $20z^6-8z^3-5z^3+2$a s v d

Question 7

Factorise the following by grouping (in pairs)

a) $2xy+10x+6y+30$a s v d
b) $3x^2-27x+6x-54$a s v d
c) $2x^3+8x^2+5x^2+20x$a s v d
d) $12xyz-12xy-9xz+9x$a s v d

Question 8

Factorise the following by grouping (in pairs)

a) $x^3+2x^2-25x+2$a s v d
b) $x^3+5x^2-8x-20$a s v d
c) $9x^3+54x^2-x-6$a s v d
d) $32x^3-80x^2-18x+45$a s v d

Question 9

Factorise the following in pairs

a) $ax+bx+ay+by+az+bz$a s v d
b) $x^3-4x^2+x^2-4x+3x-12$a s v d
c) $6ax-3bx-2ay+by+8az-4bz$a s v d
d) $8x^3-16x^2-20x^2+40x-12x+24$a s v d

Question 10

Factorise the following in triples!

a) $ax+bx+cx+ay+by+cy$a s v d
b) $x^3+x^2y+2x^2-xy^2-y^2-2y^2$a s v d