Question 3(vii)
Simplify:
(a+b+c)(a+b-c)

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Solution

$(a + b + c) (a + b - c) = a (a + b - c) + b (a + b - c) + c (a + b - c)$
$= a^{2} + a b - a c + a b + b^{2} - b c + a c + b c - c^{2}$
$= a^{2} + a b + a b - a c + a c - b c + b c + b^{2} - c^{2}$
$= a^{2} + b^{2} - c^{2} + 2 a b$

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Similar questions

Question 3(vii)
Simplify:
(a+b+c)(a+b-c)

Q. Question 30
if

a + b + c = 9

and

a b + b c + c a = 26

, find

a^{2} + b^{2} + c^{2}

Q. Prove that

∣ ∣ ∣ ∣ ∣ \begin{matrix} b c - a^{2} & c a - b^{2} & a b - c^{2} - b c + c a + a b & b c - c a + a b & b c + c a - a b (a + b) (a + c) & (b + c) (b + a) & (c + a) (c + b) \end{matrix} ∣ ∣ ∣ ∣ ∣ = 3. (b - c) (c - a) (a - b) (a + b + c) (a b + b c + c a)

Q. Show that :

∣ ∣ ∣ ∣ ∣ \begin{matrix} b c - a^{2} & c a - b^{2} & a b - c^{2} - b c + c a + c b & b c - c a + a b & b c + c a - a b (a + b) (a + c) & (b + c) (b + a) & (c + a) (c + b) \end{matrix} ∣ ∣ ∣ ∣ ∣ = 3 (b - c) (c - a) (a - b) (a + b + c) (b c + c a + a b)

Using properties of determinants prove the following questions.

$∣ ∣ ∣ ∣ \begin{matrix} 3 a & - a + b & - a + c - b + a & 3 b & - b + c - c + a & - c + b & 3 c \end{matrix} ∣ ∣ ∣ ∣ = 3 (a + b + c) (a b + b c + c a)$ .

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Addition of Algebraic Expressions

Standard VII Mathematics

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Question 3(vii) Simplify: (a+b+c)(a+b-c)

(a+b+c)(a+b−c)=a(a+b−c)+b(a+b−c)+c(a+b−c) =a2+ab−ac+ab+b2−bc+ac+bc−c2 =a2+ab+ab−ac+ac−bc+bc+b2−c2 =a2+b2−c2+2ab

Question 3(vii)
Simplify:
(a+b+c)(a+b-c)

$(a + b + c) (a + b - c) = a (a + b - c) + b (a + b - c) + c (a + b - c)$
$= a^{2} + a b - a c + a b + b^{2} - b c + a c + b c - c^{2}$
$= a^{2} + a b + a b - a c + a c - b c + b c + b^{2} - c^{2}$
$= a^{2} + b^{2} - c^{2} + 2 a b$