If a given expression is a complete square, then which of the following formulae we use to factorize it?

a^{2} + 2 a b + b^{2} = (a + b)^{2}

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

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

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(x + a) (x + b) = x^{2} + (a + b) x + a b

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Solution

The correct options are
A $a^{2} + 2 a b + b^{2} = (a + b)^{2}$
B $a^{2} - 2 a b + b^{2} = (a - b)^{2}$
If the given expression is a complete square, then we use the following formulae to factorize it.
$a^{2} + 2 a b + b^{2} = (a + b)^{2}$ and $a^{2} - 2 a b + b^{2} = (a - b)^{2}$

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Similar questions

Which of the following identity can be used to factorize $x^{2} - 4 y^{2}$ ?

Which of the following is correct?
a) $(a - b)^{2} = a^{2} + 2 a b - b^{2}$
b) $(a - b)^{2} = a^{2} - 2 a b + b^{2}$
c) $(a - b)^{2} = a^{2} - b^{2}$
d) $(a + b)^{2} = a^{2} + 2 a b - b^{2}$

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

then factor of

1 + 2 a b - (a^{2} + b^{2})

are

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

. Then factors of

1 + 2 a b - (a^{2} + b^{2})

are

Q. If A and B are square matrices of the same order, explain, why in general
(i) (A + B)² ≠ A² + 2AB + B²
(ii) (A − B)² ≠ A² − 2AB + B²
(iii) (A + B) (A − B) ≠ A² − B².

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If a given expression is a complete square, then which of the following formulae we use to factorize it?

The correct options are A a2+2ab+b2=(a+b)2 B a2−2ab+b2=(a−b)2If the given expression is a complete square, then we use the following formulae to factorize it.a2+2ab+b2=(a+b)2 and a2−2ab+b2=(a−b)2

The correct options are
A $a^{2} + 2 a b + b^{2} = (a + b)^{2}$
B $a^{2} - 2 a b + b^{2} = (a - b)^{2}$
If the given expression is a complete square, then we use the following formulae to factorize it.
$a^{2} + 2 a b + b^{2} = (a + b)^{2}$ and $a^{2} - 2 a b + b^{2} = (a - b)^{2}$