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(a+b)(a-b) Expansion and Visualisation

Simplify :i ...

Question

Simplify :
(i) $y^{2} + 24 y + 144$
(ii) $p^{2} - 7 p - 44$
(iii) $3 x^{2} + 14 x + 15$
(iv) $44 x^{2} - x - 3$

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Solution

a) $= y^{2} + 24 y + 144$
$= y^{2} + 12 y + 12 y + 144$
$= y (y + 12) + 12 (y + 12)$
$= (y + 12) (y + 12)$
$= (y + 12)^{2}$
b) $= p^{2} - 7 p - 44$
$= p^{2} - 11 p + 4 p - 44$
$= p (p - 11) + 4 (p - 11)$
$= (p - 11) (p + 4)$
c) $= 3 x^{2} + 14 x + 15$
$= 3 x^{2} + 9 x + 5 x + 15$
$= 3 x (x + 3) + 5 (x + 3)$
$= (3 x + 5) (x + 3)$
d) $= 44 x^{2} - x - 3$
$= 44 x^{2} - 12 x + 11 x - 3$
$= 4 x (11 x - 3) + 1 (11 x - 3)$
$= (4 x + 1) (11 x - 3)$

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Similar questions

y^{2} + 24 y + 144

p^{2} - 7 p - 44

3 x^{2} + 14 x + 15

44 x^{2} - x - 3

Factorise:

(i) x² + 14x + 49; (ii) 4x² + 4x + 1; (iii) a² − 10a + 25; (iv) 2x² − 24x + 72;

(v) p² − 24p + 144; (vi) x³ − 12x² + 36x.

(4) \times (7 p)

(- 4 p) \times (7 p)

(- 4 p) \times (7 p q)

(4 p^{3}) \times (- 3 p)

(4 p) \times (0)

\frac{8}{9} + \frac{- 11}{6}

\frac{- 5}{16} + \frac{7}{24}

\frac{1}{- 12} + \frac{2}{- 15}

\frac{- 8}{19} + \frac{- 4}{57}

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