Question

Factorise r2+16 r+64 using suitable identity.​

Answer 1

Answer:

(r+8)²

(r)² + 2 × 1 × 8 + (8)² Identity (a+b)²

(r+8)² or (r+8)(r+8)

Answer 2

Answer:

STEP

1

:

Trying to factor by splitting the middle term

1.1 Factoring r2-16r+64

The first term is, r2 its coefficient is 1 .

The middle term is, -16r its coefficient is -16 .

The last term, "the constant", is +64

Step-1 : Multiply the coefficient of the first term by the constant 1 • 64 = 64

Step-2 : Find two factors of 64 whose sum equals the coefficient of the middle term, which is -16 .

-64 + -1 = -65

-32 + -2 = -34

-16 + -4 = -20

-8 + -8 = -16 That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -8 and -8

r2 - 8r - 8r - 64

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

r • (r-8)

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

8 • (r-8)

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

(r-8) • (r-8)

Which is the desired factorization

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