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Factorisation by Regrouping Terms

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Question

Find the factors of the following expressions:

(1) ab + cd + ac + bd

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Solution

ab + cd + ac + bd
We can factorise this expression as:
ab + cd + ac + bd
= (ab + ac) + (cd + bd)
= a (b + c) + d (c + b)
= a (b + c) + d (b + c)
= (b + c) (a + d)

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Similar questions

Q. Find the factors of the following expressions:

(5) b² + bc + ab + ac

Let ABCD be a quadrilateral with diagonals AC and BD. Prove the following statements (Compare these with the previous problem);

(a) AB + BC + CD > AD;

(b) AB + BC + CD + DA > 2AC;

(c) AB + BC + CD + DA > 2BD;

(d) AB + BC + CD + DA > AC + BD.

Q. In Fig. 4.60, check whether AD is the bisector of ∠A of ∆ABC in each of the following:

(i) AB = 5 cm, AC = 10 cm, BD = 1.5 cm and CD = 3.5 cm
(ii) AB = 4 cm, AC = 6 cm, BD = 1.6 cm and CD = 2.4 cm
(iii) AB = 8 cm, AC = 24 cm, BD = 6 cm and BC = 24 cm
(iv) AB = 6 cm, AC = 8 cm, BD = 1.5 cm and CD = 2 cm
(v) AB = 5 cm, AC = 12 cm, BD = 2.5 cm and BC = 9 cm

Q. Find the area of shaded region

A C = B D = 7 c m

A B = C D = 1.75 c m

In the following figure, if AC = BD, then prove that AB = CD.

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Factorisation by Regrouping Terms

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