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Question

Factorise the expression
(i) ax2+bx
(ii) 7p2+21q2
(iii) 2x3+2xy2+2xz2
(iv) am2+bm2+bn2+an2
(v) (lm+l)+m+1
(vi) y(y+z)+9(y+z)
(vii) 5y220y8z+2yz
(viii) 10ab+4a+5b+2
(ix) 6xy4y+69x

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Solution

(i) ax2+bx
=x(ax+b)

(ii) 7p2+21q2
=7(p2+3q2)

(iii) 2x3+2xy2+2xz2
=2x(x2+y2+z2)

(iv) am2+bm2+bn2+an2
=m2(a+b)+n2(a+b)
=(a+b)(m2+n2)

(v) (lm+l)+m+1
=(l+1)(m+1)

(vi) y(y+z)+9(y+z)
=(y+z)(y+9)

(vii) 5y220y8z+2yz
=(y4)(5y+2z)

(viii) 10ab+4a+5b+2
=(2a+1)(5b+2)

(ix) 6xy4y+69x=3x(2y3)2(2y3)
=(2y3)(3x2)

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