Question

what are the all formulas of factorization with examples​

Answer 1

Answer:

If we factorise the quadratic, the equation can be written as (x − 5)(x + 3) = 0. But a product of two factors can only be equal to zero if one or the other factor is equal to zero.

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Example

x2 − 7x + 6 =

x2 + 7x + 6 =

x2 − 2x + 6If we factorise the quadratic, the equation can be written as (x − 5)(x + 3) = 0. But a product of two factors can only be equal to zero if one or the other factor is equal to zero.

...

Example

x2 − 7x + 6 =

x2 + 7x + 6 =

x2 − 2x + 6 =

Answer 2

All formulas of factorization :-

• (m+p)²=m²+p²+2mp

• (m−p)²=m²+p²–2mp

• (m²–p²)=(m+p)(m−p)

• (m+p)³=m³+p³+3mp(m+p)

• (m−p)³=m³–3m²p+3p²m–p³

• (a+b+c)²=a²+b²+c²+2ab+2bc+2ca

• (a−b−c)²=a²+b²+c²−2ab–2ca+2bc

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Examples :-

Q.1: Factorize the following equation, which is a quadratic type: x²+7+x6.

Solution :- Here (1 + 6) is giving 7 which is midterm coefficient.

X²+7x+6=(x+1)(x+6)

Remember that the order doesn’t matter in multiplication.

Therefore, its answer is (x + 6)(x + 1).

Q.2: Factorize the following equation, which is a quadratic type: 3x+6xy+30+60y.

Solution :- 3X + 6XY + 30 + 60Y

Taking suitable common terms,

3X(1+2Y)+ 30 (1+2Y)

i.e. (1+2Y)(3X+30)

i.e. 3(1+2Y)(X+10)

Therefore, factors: 3(1+2Y)(X+10)

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Hope it help you ✔✔