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Q: How do you factor this expression ac plus 2ad plus 2bc plus 4bd?

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(2a + b)(2c + d).

ac + 2ad + 2bc + 4bd = a(c + 2d) + 2b(c + 2d) = (a + 2b)(c + 2d) Now expand to confirm your answer: c(a + 2b) + 2d(a + 2b) = ac + 2bc + 2ad + 4bd ≡ ac + 2ad + 2bc + 4bd

4ac + 2ad + 2bc +bd = 2a*(2c + d) + b*(2c + d) = (2c + d)*(2a + b)

(2a + b)(2c + d)

(2a + b)(2c + d)

(2a + b)(2c + d)

ac + 2ad + 2bc + 4bd (ac + 2ad) + (2bc + 4bd) group the figures a(c + 2d) + 2b(c + 2d) remove the common divisors of each set (a + 2b)(c + 2d) take the figures in parentheses as one set, and add the outside figures as the other

(a - 2b)(c - 3d)

ab-2ac+b^2-2bc

a2+2ab+b2+2ac+2bc+c2+2ad+2ae+2bd+2be+2cd+2ce+d2+2de+e2

(a + b)(b - 2c)

(a + b)(b - 2c)

2bc + 8b - 3c - 12 is an expression, not an equation or inequality. It cannot, therefore have "an answer".

(3a - 2c)(b - d)

(a - 2b)(c - 3d)

3ab + 3ac + 2b2 + 2bc = 3a(b + c) + 2b(b + c) = (3a + 2b)(b + c)

3a(b+c)+2b(b+c)

4

d = a - 2bc

ac - 3ad - 2bc + 6bd = a(c - 3d) - 2b(c - 3d) = (a - 2b)(c - 3d)

(b-c)(a+b)-ac

BC' + BC' = 2BC'

No. 1a and 3d are linear, but 2bc is not. ■

d=a-2bc

GCF(12bc, ab252b2c) = 2bc