Question

Resolve into factors.
${a}^{2} + ab - {12b}^{2}$
Pls give explanation. I mean pls donot just write the answer.
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Answer 1

Answer:

$(a + 4b)(a - 3b)$

Step-by-step explanation:

${a}^{2} + ab - 12{b}^{2} \\ = {a}^{2} + (4 - 3)ab - 12 {b}^{2} \\ = {a}^{2} + 4ab - 3ab - 12 {b}^{2} \\ = a(a + 4b) - 3b(a + 4b) \\ = (a + 4b)(a - 3b)$

Answer 2

Solution :-

→ a² + ab - 12b²

Splitting The Middle Term,

→ a² - 3ab + 4ab - 12b²

→ (a² - 3ab) + (4ab - 12b²)

Taking common Now,

→ a(a - 3b) + 4b(a - 3b)

Taking (a - 3b) common Now,

→ (a - 3b)(a + 4b) (Ans.)

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Extra :-

Splitting The Middle Term Method :- ax² + bx + c = 0

• Find the product of 1st and last term = a*c .
• Find the factors of a*c in such way that
• addition or subtraction of that factors is
• the middle term = b . (Splitting of middle term).
• Write the center term using the sum of the
• two new factors, including the proper signs.
• Group the terms to form pairs - the first two
• terms and the last two terms. Factor each pair by finding common factors.
• Factor out the shared (common) binomial parenthesis.

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