Question

giải giúp em vs ạ

Answer 1

12) a) \(4x^2+4x+1=\left(2x\right)^2+2.2x.1+1^2=\left(2x+1\right)^2\)

b) \(y^2-10y+25=y^2-2.5.y+5^2=\left(y-5\right)^2\)

c) \(a^2+ab+\dfrac{1}{4}b^2=a^2+2.a.\dfrac{1}{2}b+\left(\dfrac{1}{2}b\right)^2=\left(a+\dfrac{1}{2}b\right)^2\)

d) \(4x^2-12xy+9y^2=\left(2x\right)^2-2.2x.3y+\left(3y\right)^2=\left(2x-3y\right)^2\)

16) a) \(\left(2x+1\right)^2-x^2-4x+5\)

\(=4x^2+4x+1-x^2-4x+5\)

\(=3x^2+6=3\left(x^2+1\right)\)

b) \(\left(4-3x\right)^2-\left(2x+3\right)\left(3-2x\right)\)

\(=16-24x+9x^2+\left(2x+3\right)\left(2x-3\right)\)

\(=16-24x+9x^2+4x^2-9\)

\(=13x^2-24x+7\)

c) \(2\left(x-1\right)^2-3\left(x+3\right)^2+\left(2x-1\right)\left(2x+1\right)\)

\(=2\left(x^2-2x+1\right)-3\left(x^2+6x+9\right)+4x^2-1\)

\(=2x^2-4x+2-3x^2-18x-27+4x^2-1\)

\(=3x^2-22x-26\)

Answer 2

14:

a: \(107^2-93^2=\left(107-93\right)\left(107+93\right)\)

\(=14\cdot200=2800\)

b: \(106\cdot94=\left(100+6\right)\left(100-6\right)=100^2-6^2\)

=10000-36

=9964

c: \(102^2=\left(100+2\right)^2=100^2+2\cdot100\cdot2+2^2\)

\(=10000+400+4=10404\)

d: \(199^2=\left(200-1\right)^2\)

\(=200^2-2\cdot200\cdot1+1^2\)

=40000-400+1

=39601

e: \(234^2-233\cdot235\)

\(=234^2-\left(234-1\right)\left(234+1\right)\)

\(=234^2-\left(234^2-1\right)=1\)

f: \(788\cdot790-789^2=789^2-1-789^2=-1\)

g: \(234^2+132\cdot234+66^2\)

\(=234^2+2\cdot234\cdot66+66^2\)

\(=\left(234+66\right)^2=300^2=90000\)

h: \(368^2-68\cdot736+68^2\)

\(=368^2-2\cdot368\cdot68+68^2\)

\(=\left(368-68\right)^2=300^2=90000\)

15:

a: \(A=9x^2-4=\left(3x-2\right)\left(3x+2\right)\)

Thay \(x=\dfrac{2}{3}\) vào A, ta được:

\(A=\left(3\cdot\dfrac{2}{3}-2\right)\left(3\cdot\dfrac{2}{3}+2\right)=\left(2-2\right)\left(2+2\right)=0\cdot4=0\)

b: \(B=x^2+8x+16=\left(x+4\right)^2\)

Khi x=26 thì \(B=\left(26+4\right)^2=30^2=900\)

c: \(C=2x^2-12xy+18y^2\)

\(=2\left(x^2-6xy+9y^2\right)\)

\(=2\left[x^2-2\cdot x\cdot3y+\left(3y\right)^2\right]\)

\(=2\left(x-3y\right)^2\)

Thay x=39;y=12 vào C, ta được:

\(C=2\left[39-3\cdot12\right]^2=2\cdot\left(39-36\right)^2=2\cdot3^2=18\)

d: \(D=\left(x+y\right)^2\)

\(=\left(x-y\right)^2+4xy\)

\(=10^2+4\cdot24=100+96=196\)