Step 1: Take (a+b) as single term and expand. (a+b c)^2 = (a+b)^2 2 × (a+b) × c + (c)^2 = (a+b)^2 2ac 2bc + c^2 Step 2: Now apply the formula of square o ...

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Standard XII

Mathematics

Inverse of a Matrix

Expand :a+b-c...

Question

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

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Solution

Step 1: Take $(a + b)$ as single term and expand.
$(a + b - c)^{2} = (a + b)^{2} - 2 \times (a + b) \times c + (c)^{2}$
$= (a + b)^{2} - 2 a c - 2 b c + c^{2}$

Step 2: Now apply the formula of square of sum of two terms.
$(a + b - c)^{2} = a^{2} + b^{2} + 2 a b - 2 a c - 2 b c + c^{2}$
$[∵ (a + b)^{2} = a^{2} + 2 \times a \times b + b^{2}]$
Hence, $(a + b - c)^{2} = a^{2} + b^{2} + c^{2} + 2 a b - 2 a c - 2 b c$

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Similar questions

Q. Write 5 examples of the form (a + b + c)² and expand them using the formula.

Q. Simplify:

(i) (a +b + c)² + (a − b + c)²

(ii) (a +b + c)² − (a − b + c)2

(iii) (a +b + c)²+ (a − b + c)² + (a +b − c)²

(iv) (2x + p − c)²− (2x − p + c)²

(v) (x² + y²− z²) − (x² − y² + z²)²

Q. Expand :

(a + b + c)^{2}

Q. Expand:

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

Q. Expand the following formulas

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

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Inverse of a Matrix

Standard XII Mathematics

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Expand : (a+b−c)2

Step 1: Take (a+b) as single term and expand. (a+b−c)2=(a+b)2−2×(a+b)×c+(c)2 =(a+b)2−2ac−2bc+c2 Step 2: Now apply the formula of square of sum of two terms. (a+b−c)2=a2+b2+2ab−2ac−2bc+c2 [∵(a+b)2=a2+2×a×b+b2] Hence, (a+b−c)2=a2+b2+c2+2ab−2ac−2bc

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