# Test: Factorisation I - Challenging

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Question 1:   Factorise: $14x+42y$
$7\left(2x+6\right)$
$14\left(x+3y\right)$
$56\left(x+y\right)$
$56xy$
Question 2:   Factorise: $1.14a+5.7{a}^{2}$
$6.84a\left(a+1\right)$
$6.14\left(a+1\right)$
$a\left(1.12+5.7a\right)$
$1.14a\left(5a+1\right)$
Question 3:   Factorise: $54p-3q$
$51pq$
$3\left(18p-q\right)$
$3\left(16p-q\right)$
$18\left(3p-q\right)$
Question 4:   Factorise: $13{a}^{2}b-14ab+12a$
$11{a}^{2}$
$a\left(13ab-14b+12\right)$
$a\left(13ab-14b+1\right)$
$12a\left(ab-2b+1\right)$
Question 5:   Factorise: $3{x}^{3}{y}^{2}+27{x}^{2}{y}^{2}-18x{y}^{3}$
$xy\left({x}^{2}y+27xy-18y{}^{2}\right)$
$6x{y}^{2}\left({x}^{2}+2x-3y\right)$
$12{x}^{4}y$
$3x{y}^{2}\left({x}^{2}+9x-6y\right)$
Question 6:   Factorise: $2{a}^{3}b-4{b}^{3}a+8{a}^{2}{b}^{2}$
$ab\left(2a-4{b}^{2}+8ab\right)$
$2ab\left({a}^{2}-2{b}^{2}+4ab\right)$
$6{a}^{4}$
$2{a}^{2}b\left(a-2{b}^{2}+4b\right)$
Question 7:   Factorise: $2x+px+2y+py$
$\left(2+p\right)\left(x+y\right)$
$2{x}^{2}p+2{y}^{2}p$
Cannot be factored
$x\left(2+p\right)+y\left(2+p\right)$
Question 8:   Factorise: $2px-qx-2py+qy$
$\left(2p-q\right)\left(x-y\right)$
$2\left(px-qx\right)-2\left(py+qy\right)$
$x\left(2p-q\right)-y\left(2p+q\right)$
$2\left(p-q\right)-2\left(p+q\right)$
Question 9:   Factorise: $2ax+bx-2ay-by$
$2\left(a+b\right)-2\left(x+y\right)$
$x\left(2a+b-2ay-by\right)$
$\left(2a+b\right)\left(x-y\right)$
$2\left(a+b\right)\left(x-y\right)$
Question 10:   Factorise: ${x}^{2}+x-6$
$\left(x+1\right)\left(x-6\right)$
$\left(x-3\right)\left(x-2\right)$
$\left(x-3\right)\left(x+2\right)$
$\left(x+3\right)\left(x-2\right)$