Question

49b^2 + 84bd + 36d^2​

Answer 1

Answer:

Changes made to your input should not affect the solution:

(1): "b2" was replaced by "b^2".

STEP

1

:

Equation at the end of step 1

(72b2 + 84b) + 36

STEP

2

:

Trying to factor by splitting the middle term

2.1 Factoring 49b2+84b+36

The first term is, 49b2 its coefficient is 49 .

The middle term is, +84b its coefficient is 84 .

The last term, "the constant", is +36

Step-1 : Multiply the coefficient of the first term by the constant 49 • 36 = 1764

Step-2 : Find two factors of 1764 whose sum equals the coefficient of the middle term, which is 84 .

-1764 + -1 = -1765

-882 + -2 = -884

-588 + -3 = -591

-441 + -4 = -445

-294 + -6 = -300

-252 + -7 = -259

-196 + -9 = -205

-147 + -12 = -159

-126 + -14 = -140

-98 + -18 = -116

-84 + -21 = -105

-63 + -28 = -91

-49 + -36 = -85

-42 + -42 = -84

-36 + -49 = -85

-28 + -63 = -91

-21 + -84 = -105

-18 + -98 = -116

-14 + -126 = -140

-12 + -147 = -159

-9 + -196 = -205

-7 + -252 = -259

-6 + -294 = -300

-4 + -441 = -445

-3 + -588 = -591

-2 + -882 = -884

-1 + -1764 = -1765

1 + 1764 = 1765

2 + 882 = 884

3 + 588 = 591

4 + 441 = 445

6 + 294 = 300

7 + 252 = 259

9 + 196 = 205

12 + 147 = 159

14 + 126 = 140

18 + 98 = 116

21 + 84 = 105

28 + 63 = 91

36 + 49 = 85

42 + 42 = 84 That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, 42 and 42

49b2 + 42b + 42b + 36

Step-4 : Add up the first 2 terms, pulling out like factors :

7b • (7b+6)

Add up the last 2 terms, pulling out common factors :

6 • (7b+6)

Step-5 : Add up the four terms of step 4 :

(7b+6) • (7b+6)

Which is the desired factorization

Multiplying Exponential Expressions:

2.2 Multiply (7b+6) by (7b+6)

The rule says : To multiply exponential expressions which have the same base, add up their exponents.

In our case, the common base is (7b+6) and the exponents are :

1 , as (7b+6) is the same number as (7b+6)1

and 1 , as (7b+6) is the same number as (7b+6)1

The product is therefore, (7b+6)(1+1) = (7b+6)2

Final result :

(7b + 6)2

Answer 2

$\large\mathfrak \pink{Solution:-}$

$\underline \mathbb{FORMULA:-}$

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

$\underline \mathbb{BY \: THE \: PROBLEM:-}$

${49b}^{2} + 84bd + {36d}^{2} \\ \\ \implies \: (7b) {}^{2} +2 \times( 7 b)\times( 6d)+ {(6d)}^{2} \\ \\ \implies \:(7b + 6d) {}^{2}$

$\underline \mathbb{ANSWER:-}$

$\implies \boxed{(7b + 6d) {}^{2} }$